Solve frac{x^{2}+x-56}{x^2+x-90}*x^2+14x+45/x^2-x-42divx+5/x^2+16x+60

$$\frac { x ^ { 2 } + x - 56 } { x ^ { 2 } + x - 90 } \cdot \frac { x ^ { 2 } + 14 x + 45 } { x ^ { 2 } - x - 42 } \div \frac { x + 5 } { x ^ { 2 } + 16 x + 60 }$$

Evaluate

$$\frac{\left(x+8\right)\left(x+9\right)}{x-9}$$

Short Solution Steps

Multiply \frac{x^{2}+x-56}{x^{2}+x-90} times \frac{x^{2}+14x+45}{x^{2}-x-42} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\left(x^{2}+x-56\right)\left(x^{2}+14x+45\right)}{\left(x^{2}+x-90\right)\left(x^{2}-x-42\right)}}{\frac{x+5}{x^{2}+16x+60}}$$

Divide \frac{\left(x^{2}+x-56\right)\left(x^{2}+14x+45\right)}{\left(x^{2}+x-90\right)\left(x^{2}-x-42\right)} by \frac{x+5}{x^{2}+16x+60} by multiplying \frac{\left(x^{2}+x-56\right)\left(x^{2}+14x+45\right)}{\left(x^{2}+x-90\right)\left(x^{2}-x-42\right)} by the reciprocal of \frac{x+5}{x^{2}+16x+60}.

$$\frac{\left(x^{2}+x-56\right)\left(x^{2}+14x+45\right)\left(x^{2}+16x+60\right)}{\left(x^{2}+x-90\right)\left(x^{2}-x-42\right)\left(x+5\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-7\right)\left(x+5\right)\left(x+6\right)\left(x+8\right)\left(x+9\right)\left(x+10\right)}{\left(x-9\right)\left(x-7\right)\left(x+5\right)\left(x+6\right)\left(x+10\right)}$$

Cancel out \left(x-7\right)\left(x+5\right)\left(x+6\right)\left(x+10\right) in both numerator and denominator.

$$\frac{\left(x+8\right)\left(x+9\right)}{x-9}$$

Expand the expression.

$$\frac{x^{2}+17x+72}{x-9}$$

Expand

$$\frac{x^{2}+17x+72}{x-9}$$

Short Solution Steps

Multiply \frac{x^{2}+x-56}{x^{2}+x-90} times \frac{x^{2}+14x+45}{x^{2}-x-42} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\left(x^{2}+x-56\right)\left(x^{2}+14x+45\right)}{\left(x^{2}+x-90\right)\left(x^{2}-x-42\right)}}{\frac{x+5}{x^{2}+16x+60}}$$

Divide \frac{\left(x^{2}+x-56\right)\left(x^{2}+14x+45\right)}{\left(x^{2}+x-90\right)\left(x^{2}-x-42\right)} by \frac{x+5}{x^{2}+16x+60} by multiplying \frac{\left(x^{2}+x-56\right)\left(x^{2}+14x+45\right)}{\left(x^{2}+x-90\right)\left(x^{2}-x-42\right)} by the reciprocal of \frac{x+5}{x^{2}+16x+60}.

$$\frac{\left(x^{2}+x-56\right)\left(x^{2}+14x+45\right)\left(x^{2}+16x+60\right)}{\left(x^{2}+x-90\right)\left(x^{2}-x-42\right)\left(x+5\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-7\right)\left(x+5\right)\left(x+6\right)\left(x+8\right)\left(x+9\right)\left(x+10\right)}{\left(x-9\right)\left(x-7\right)\left(x+5\right)\left(x+6\right)\left(x+10\right)}$$

Cancel out \left(x-7\right)\left(x+5\right)\left(x+6\right)\left(x+10\right) in both numerator and denominator.

$$\frac{\left(x+8\right)\left(x+9\right)}{x-9}$$

Expand the expression.

$$\frac{x^{2}+17x+72}{x-9}$$