Solve (a ^ 2 - 1)/(2a ^ 2 - 3a) * (5a ^ 2 + 2a)/(5a ^ 2 - 3a - 2) | 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

$$\frac{a^{2}-1}{2a^{2}-3a}\times\frac{5a^{2}+2a}{5a^{2}-3a-2}$$

Evaluate

$\frac{a+1}{2a-3}$

Short Solution Steps

Factor the expressions that are not already factored in $\frac{5a^{2}+2a}{5a^{2}-3a-2}$.

$$\frac{a^{2}-1}{2a^{2}-3a}\times \frac{a\left(5a+2\right)}{\left(a-1\right)\left(5a+2\right)}$$

Cancel out $5a+2$ in both numerator and denominator.

$$\frac{a^{2}-1}{2a^{2}-3a}\times \frac{a}{a-1}$$

Multiply $\frac{a^{2}-1}{2a^{2}-3a}$ times $\frac{a}{a-1}$ by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

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

Cancel out $a\left(a-1\right)$ in both numerator and denominator.

$$\frac{a+1}{2a-3}$$

Expand

$\frac{a+1}{2a-3}$

Short Solution Steps

Factor the expressions that are not already factored in $\frac{5a^{2}+2a}{5a^{2}-3a-2}$.

$$\frac{a^{2}-1}{2a^{2}-3a}\times \frac{a\left(5a+2\right)}{\left(a-1\right)\left(5a+2\right)}$$

Cancel out $5a+2$ in both numerator and denominator.

$$\frac{a^{2}-1}{2a^{2}-3a}\times \frac{a}{a-1}$$

Multiply $\frac{a^{2}-1}{2a^{2}-3a}$ times $\frac{a}{a-1}$ by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

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

Cancel out $a\left(a-1\right)$ in both numerator and denominator.

$$\frac{a+1}{2a-3}$$