Solve x+4/x-3/frac{x-8{x+5}}

$$\frac { \frac { x + 4 } { x - 3 } } { \frac { x - 8 } { x + 5 } }$$

Evaluate

$$\frac{\left(x+4\right)\left(x+5\right)}{\left(x-8\right)\left(x-3\right)}$$

Short Solution Steps

Divide \frac{x+4}{x-3} by \frac{x-8}{x+5} by multiplying \frac{x+4}{x-3} by the reciprocal of \frac{x-8}{x+5}.

$$\frac{\left(x+4\right)\left(x+5\right)}{\left(x-3\right)\left(x-8\right)}$$

Apply the distributive property by multiplying each term of x+4 by each term of x+5.

$$\frac{x^{2}+5x+4x+20}{\left(x-3\right)\left(x-8\right)}$$

Combine 5x and 4x to get 9x.

$$\frac{x^{2}+9x+20}{\left(x-3\right)\left(x-8\right)}$$

Apply the distributive property by multiplying each term of x-3 by each term of x-8.

$$\frac{x^{2}+9x+20}{x^{2}-8x-3x+24}$$

Combine -8x and -3x to get -11x.

$$\frac{x^{2}+9x+20}{x^{2}-11x+24}$$

Expand

$$\frac{x^{2}+9x+20}{\left(x-8\right)\left(x-3\right)}$$

Short Solution Steps

Divide \frac{x+4}{x-3} by \frac{x-8}{x+5} by multiplying \frac{x+4}{x-3} by the reciprocal of \frac{x-8}{x+5}.

$$\frac{\left(x+4\right)\left(x+5\right)}{\left(x-3\right)\left(x-8\right)}$$

Apply the distributive property by multiplying each term of x+4 by each term of x+5.

$$\frac{x^{2}+5x+4x+20}{\left(x-3\right)\left(x-8\right)}$$

Combine 5x and 4x to get 9x.

$$\frac{x^{2}+9x+20}{\left(x-3\right)\left(x-8\right)}$$

Apply the distributive property by multiplying each term of x-3 by each term of x-8.

$$\frac{x^{2}+9x+20}{x^{2}-8x-3x+24}$$

Combine -8x and -3x to get -11x.

$$\frac{x^{2}+9x+20}{x^{2}-11x+24}$$