Solve (y ^ 3 - 1)/(y + 1/(y + 1)) | 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

$$\frac{y^{3}-1}{y+\frac{1}{y+1}}$$

Evaluate

$y^{2}-1$

Short Solution Steps

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

$$\frac{y^{3}-1}{\frac{y\left(y+1\right)}{y+1}+\frac{1}{y+1}}$$

Since $\frac{y\left(y+1\right)}{y+1}$ and $\frac{1}{y+1}$ have the same denominator, add them by adding their numerators.

$$\frac{y^{3}-1}{\frac{y\left(y+1\right)+1}{y+1}}$$

Do the multiplications in $y\left(y+1\right)+1$.

$$\frac{y^{3}-1}{\frac{y^{2}+y+1}{y+1}}$$

Divide $y^{3}-1$ by $\frac{y^{2}+y+1}{y+1}$ by multiplying $y^{3}-1$ by the reciprocal of $\frac{y^{2}+y+1}{y+1}$.

$$\frac{\left(y^{3}-1\right)\left(y+1\right)}{y^{2}+y+1}$$

Factor the expressions that are not already factored.

$$\frac{\left(y-1\right)\left(y+1\right)\left(y^{2}+y+1\right)}{y^{2}+y+1}$$

Cancel out $y^{2}+y+1$ in both numerator and denominator.

$$\left(y-1\right)\left(y+1\right)$$

Expand the expression.

$$y^{2}-1$$

Expand

$y^{2}-1$

Short Solution Steps

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

$$\frac{y^{3}-1}{\frac{y\left(y+1\right)}{y+1}+\frac{1}{y+1}}$$

Since $\frac{y\left(y+1\right)}{y+1}$ and $\frac{1}{y+1}$ have the same denominator, add them by adding their numerators.

$$\frac{y^{3}-1}{\frac{y\left(y+1\right)+1}{y+1}}$$

Do the multiplications in $y\left(y+1\right)+1$.

$$\frac{y^{3}-1}{\frac{y^{2}+y+1}{y+1}}$$

Divide $y^{3}-1$ by $\frac{y^{2}+y+1}{y+1}$ by multiplying $y^{3}-1$ by the reciprocal of $\frac{y^{2}+y+1}{y+1}$.

$$\frac{\left(y^{3}-1\right)\left(y+1\right)}{y^{2}+y+1}$$

Factor the expressions that are not already factored.

$$\frac{\left(y-1\right)\left(y+1\right)\left(y^{2}+y+1\right)}{y^{2}+y+1}$$

Cancel out $y^{2}+y+1$ in both numerator and denominator.

$$\left(y-1\right)\left(y+1\right)$$

Expand the expression.

$$y^{2}-1$$