Solve (1 + 1/(x + 1))(1 + 1/(x + 2))(1 + 1/(x + 3))(1 + 1/(x + 4)) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$(1+\frac{1}{x+1})(1+\frac{1}{x+2})(1+\frac{1}{x+3})(1+\frac{1}{x+4})$$

Evaluate

$\frac{x+5}{x+1}$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply $1$ times $\frac{x+1}{x+1}$.

$$\left(\frac{x+1}{x+1}+\frac{1}{x+1}\right)\left(1+\frac{1}{x+2}\right)\left(1+\frac{1}{x+3}\right)\left(1+\frac{1}{x+4}\right)$$

Since $\frac{x+1}{x+1}$ and $\frac{1}{x+1}$ have the same denominator, add them by adding their numerators.

$$\frac{x+1+1}{x+1}\left(1+\frac{1}{x+2}\right)\left(1+\frac{1}{x+3}\right)\left(1+\frac{1}{x+4}\right)$$

Combine like terms in $x+1+1$.

$$\frac{x+2}{x+1}\left(1+\frac{1}{x+2}\right)\left(1+\frac{1}{x+3}\right)\left(1+\frac{1}{x+4}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $1$ times $\frac{x+2}{x+2}$.

$$\frac{x+2}{x+1}\left(\frac{x+2}{x+2}+\frac{1}{x+2}\right)\left(1+\frac{1}{x+3}\right)\left(1+\frac{1}{x+4}\right)$$

Since $\frac{x+2}{x+2}$ and $\frac{1}{x+2}$ have the same denominator, add them by adding their numerators.

$$\frac{x+2}{x+1}\times \frac{x+2+1}{x+2}\left(1+\frac{1}{x+3}\right)\left(1+\frac{1}{x+4}\right)$$

Combine like terms in $x+2+1$.

$$\frac{x+2}{x+1}\times \frac{x+3}{x+2}\left(1+\frac{1}{x+3}\right)\left(1+\frac{1}{x+4}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $1$ times $\frac{x+3}{x+3}$.

$$\frac{x+2}{x+1}\times \frac{x+3}{x+2}\left(\frac{x+3}{x+3}+\frac{1}{x+3}\right)\left(1+\frac{1}{x+4}\right)$$

Since $\frac{x+3}{x+3}$ and $\frac{1}{x+3}$ have the same denominator, add them by adding their numerators.

$$\frac{x+2}{x+1}\times \frac{x+3}{x+2}\times \frac{x+3+1}{x+3}\left(1+\frac{1}{x+4}\right)$$

Combine like terms in $x+3+1$.

$$\frac{x+2}{x+1}\times \frac{x+3}{x+2}\times \frac{x+4}{x+3}\left(1+\frac{1}{x+4}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $1$ times $\frac{x+4}{x+4}$.

$$\frac{x+2}{x+1}\times \frac{x+3}{x+2}\times \frac{x+4}{x+3}\left(\frac{x+4}{x+4}+\frac{1}{x+4}\right)$$

Since $\frac{x+4}{x+4}$ and $\frac{1}{x+4}$ have the same denominator, add them by adding their numerators.

$$\frac{x+2}{x+1}\times \frac{x+3}{x+2}\times \frac{x+4}{x+3}\times \frac{x+4+1}{x+4}$$

Combine like terms in $x+4+1$.

$$\frac{x+2}{x+1}\times \frac{x+3}{x+2}\times \frac{x+4}{x+3}\times \frac{x+5}{x+4}$$

Multiply $\frac{x+2}{x+1}$ times $\frac{x+3}{x+2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+2\right)\left(x+3\right)}{\left(x+1\right)\left(x+2\right)}\times \frac{x+4}{x+3}\times \frac{x+5}{x+4}$$

Cancel out $x+2$ in both numerator and denominator.

$$\frac{x+3}{x+1}\times \frac{x+4}{x+3}\times \frac{x+5}{x+4}$$

Multiply $\frac{x+3}{x+1}$ times $\frac{x+4}{x+3}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+3\right)\left(x+4\right)}{\left(x+1\right)\left(x+3\right)}\times \frac{x+5}{x+4}$$

Cancel out $x+3$ in both numerator and denominator.

$$\frac{x+4}{x+1}\times \frac{x+5}{x+4}$$

Multiply $\frac{x+4}{x+1}$ times $\frac{x+5}{x+4}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+4\right)\left(x+5\right)}{\left(x+1\right)\left(x+4\right)}$$

Cancel out $x+4$ in both numerator and denominator.

$$\frac{x+5}{x+1}$$

Expand

$\frac{x+5}{x+1}$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply $1$ times $\frac{x+1}{x+1}$.

$$\left(\frac{x+1}{x+1}+\frac{1}{x+1}\right)\left(1+\frac{1}{x+2}\right)\left(1+\frac{1}{x+3}\right)\left(1+\frac{1}{x+4}\right)$$

Since $\frac{x+1}{x+1}$ and $\frac{1}{x+1}$ have the same denominator, add them by adding their numerators.

$$\frac{x+1+1}{x+1}\left(1+\frac{1}{x+2}\right)\left(1+\frac{1}{x+3}\right)\left(1+\frac{1}{x+4}\right)$$

Combine like terms in $x+1+1$.

$$\frac{x+2}{x+1}\left(1+\frac{1}{x+2}\right)\left(1+\frac{1}{x+3}\right)\left(1+\frac{1}{x+4}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $1$ times $\frac{x+2}{x+2}$.

$$\frac{x+2}{x+1}\left(\frac{x+2}{x+2}+\frac{1}{x+2}\right)\left(1+\frac{1}{x+3}\right)\left(1+\frac{1}{x+4}\right)$$

Since $\frac{x+2}{x+2}$ and $\frac{1}{x+2}$ have the same denominator, add them by adding their numerators.

$$\frac{x+2}{x+1}\times \frac{x+2+1}{x+2}\left(1+\frac{1}{x+3}\right)\left(1+\frac{1}{x+4}\right)$$

Combine like terms in $x+2+1$.

$$\frac{x+2}{x+1}\times \frac{x+3}{x+2}\left(1+\frac{1}{x+3}\right)\left(1+\frac{1}{x+4}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $1$ times $\frac{x+3}{x+3}$.

$$\frac{x+2}{x+1}\times \frac{x+3}{x+2}\left(\frac{x+3}{x+3}+\frac{1}{x+3}\right)\left(1+\frac{1}{x+4}\right)$$

Since $\frac{x+3}{x+3}$ and $\frac{1}{x+3}$ have the same denominator, add them by adding their numerators.

$$\frac{x+2}{x+1}\times \frac{x+3}{x+2}\times \frac{x+3+1}{x+3}\left(1+\frac{1}{x+4}\right)$$

Combine like terms in $x+3+1$.

$$\frac{x+2}{x+1}\times \frac{x+3}{x+2}\times \frac{x+4}{x+3}\left(1+\frac{1}{x+4}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $1$ times $\frac{x+4}{x+4}$.

$$\frac{x+2}{x+1}\times \frac{x+3}{x+2}\times \frac{x+4}{x+3}\left(\frac{x+4}{x+4}+\frac{1}{x+4}\right)$$

Since $\frac{x+4}{x+4}$ and $\frac{1}{x+4}$ have the same denominator, add them by adding their numerators.

$$\frac{x+2}{x+1}\times \frac{x+3}{x+2}\times \frac{x+4}{x+3}\times \frac{x+4+1}{x+4}$$

Combine like terms in $x+4+1$.

$$\frac{x+2}{x+1}\times \frac{x+3}{x+2}\times \frac{x+4}{x+3}\times \frac{x+5}{x+4}$$

Multiply $\frac{x+2}{x+1}$ times $\frac{x+3}{x+2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+2\right)\left(x+3\right)}{\left(x+1\right)\left(x+2\right)}\times \frac{x+4}{x+3}\times \frac{x+5}{x+4}$$

Cancel out $x+2$ in both numerator and denominator.

$$\frac{x+3}{x+1}\times \frac{x+4}{x+3}\times \frac{x+5}{x+4}$$

Multiply $\frac{x+3}{x+1}$ times $\frac{x+4}{x+3}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+3\right)\left(x+4\right)}{\left(x+1\right)\left(x+3\right)}\times \frac{x+5}{x+4}$$

Cancel out $x+3$ in both numerator and denominator.

$$\frac{x+4}{x+1}\times \frac{x+5}{x+4}$$

Multiply $\frac{x+4}{x+1}$ times $\frac{x+5}{x+4}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+4\right)\left(x+5\right)}{\left(x+1\right)\left(x+4\right)}$$

Cancel out $x+4$ in both numerator and denominator.

$$\frac{x+5}{x+1}$$