Solve (y ^ 2 + y + 1)/(y + 1) * (y - 1)/(y + 1) * (y ^ 2 - 1)/(y ^ 3 - 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

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

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in $\frac{y^{2}-1}{y^{3}-1}$.

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

Cancel out $y-1$ in both numerator and denominator.

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

Multiply $\frac{y^{2}+y+1}{y+1}$ times $\frac{y-1}{y+1}$ by multiplying numerator times numerator and denominator times denominator.

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

Multiply $\frac{\left(y^{2}+y+1\right)\left(y-1\right)}{\left(y+1\right)\left(y+1\right)}$ times $\frac{y+1}{y^{2}+y+1}$ by multiplying numerator times numerator and denominator times denominator.

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

Cancel out $\left(y+1\right)\left(y^{2}+y+1\right)$ in both numerator and denominator.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in $\frac{y^{2}-1}{y^{3}-1}$.

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

Cancel out $y-1$ in both numerator and denominator.

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

Multiply $\frac{y^{2}+y+1}{y+1}$ times $\frac{y-1}{y+1}$ by multiplying numerator times numerator and denominator times denominator.

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

Multiply $\frac{\left(y^{2}+y+1\right)\left(y-1\right)}{\left(y+1\right)\left(y+1\right)}$ times $\frac{y+1}{y^{2}+y+1}$ by multiplying numerator times numerator and denominator times denominator.

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

Cancel out $\left(y+1\right)\left(y^{2}+y+1\right)$ in both numerator and denominator.

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