Solve (pq - pr)/(r ^ 2 - 1) / ((q ^ 2 - r ^ 2)/(r ^ 2 + r)) | 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

$$\frac{pq-pr}{r^{2}-1}\div\frac{q^{2}-r^{2}}{r^{2}+r}$$

Evaluate

$\frac{pr}{\left(r-1\right)\left(q+r\right)}$
$r\neq 0\text{ and }|r|\neq 1\text{ and }|q|\neq |r|$

Short Solution Steps

Divide $\frac{pq-pr}{r^{2}-1}$ by $\frac{q^{2}-r^{2}}{r^{2}+r}$ by multiplying $\frac{pq-pr}{r^{2}-1}$ by the reciprocal of $\frac{q^{2}-r^{2}}{r^{2}+r}$.

$$\frac{\left(pq-pr\right)\left(r^{2}+r\right)}{\left(r^{2}-1\right)\left(q^{2}-r^{2}\right)}$$

Factor the expressions that are not already factored.

$$\frac{pr\left(r+1\right)\left(q-r\right)}{\left(r-1\right)\left(r+1\right)\left(q+r\right)\left(q-r\right)}$$

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

$$\frac{pr}{\left(r-1\right)\left(q+r\right)}$$

Expand the expression.

$$\frac{pr}{qr-q+r^{2}-r}$$

Expand

$\frac{pr}{\left(r-1\right)\left(q+r\right)}$
$r\neq 0\text{ and }|r|\neq 1\text{ and }|q|\neq |r|$

Short Solution Steps

Divide $\frac{pq-pr}{r^{2}-1}$ by $\frac{q^{2}-r^{2}}{r^{2}+r}$ by multiplying $\frac{pq-pr}{r^{2}-1}$ by the reciprocal of $\frac{q^{2}-r^{2}}{r^{2}+r}$.

$$\frac{\left(pq-pr\right)\left(r^{2}+r\right)}{\left(r^{2}-1\right)\left(q^{2}-r^{2}\right)}$$

Factor the expressions that are not already factored.

$$\frac{pr\left(r+1\right)\left(q-r\right)}{\left(r-1\right)\left(r+1\right)\left(q+r\right)\left(q-r\right)}$$

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

$$\frac{pr}{\left(r-1\right)\left(q+r\right)}$$

Expand the expression.

$$\frac{pr}{qr-q+r^{2}-r}$$