Solve x^2+x-20/x^2-10x+25divx^2-16/x^2-25

$$\frac { x ^ { 2 } + x - 20 } { x ^ { 2 } - 10 x + 25 } \div \frac { x ^ { 2 } - 16 } { x ^ { 2 } - 25 }$$

Evaluate

$$\frac{\left(x+5\right)^{2}}{\left(x-5\right)\left(x+4\right)}$$

Short Solution Steps

Divide \frac{x^{2}+x-20}{x^{2}-10x+25} by \frac{x^{2}-16}{x^{2}-25} by multiplying \frac{x^{2}+x-20}{x^{2}-10x+25} by the reciprocal of \frac{x^{2}-16}{x^{2}-25}.

$$\frac{\left(x^{2}+x-20\right)\left(x^{2}-25\right)}{\left(x^{2}-10x+25\right)\left(x^{2}-16\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-5\right)\left(x-4\right)\left(x+5\right)^{2}}{\left(x-4\right)\left(x+4\right)\left(x-5\right)^{2}}$$

Cancel out \left(x-5\right)\left(x-4\right) in both numerator and denominator.

$$\frac{\left(x+5\right)^{2}}{\left(x-5\right)\left(x+4\right)}$$

Expand the expression.

$$\frac{x^{2}+10x+25}{x^{2}-x-20}$$

Expand

$$\frac{x^{2}+10x+25}{\left(x-5\right)\left(x+4\right)}$$

Short Solution Steps

Divide \frac{x^{2}+x-20}{x^{2}-10x+25} by \frac{x^{2}-16}{x^{2}-25} by multiplying \frac{x^{2}+x-20}{x^{2}-10x+25} by the reciprocal of \frac{x^{2}-16}{x^{2}-25}.

$$\frac{\left(x^{2}+x-20\right)\left(x^{2}-25\right)}{\left(x^{2}-10x+25\right)\left(x^{2}-16\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-5\right)\left(x-4\right)\left(x+5\right)^{2}}{\left(x-4\right)\left(x+4\right)\left(x-5\right)^{2}}$$

Cancel out \left(x-5\right)\left(x-4\right) in both numerator and denominator.

$$\frac{\left(x+5\right)^{2}}{\left(x-5\right)\left(x+4\right)}$$

Expand the expression.

$$\frac{x^{2}+10x+25}{x^{2}-x-20}$$