Solve [x+9(x-9)]+[-5x(2x-9)]/-5x(x+4)(x-9)

$$\frac { [ x + 9 ( x - 9 ) ] + [ - 5 x ( 2 x - 9 ) ] } { - 5 x ( x + 4 ) ( x - 9 ) }$$

Evaluate

$$-\frac{-10x^{2}+55x-81}{5x\left(x-9\right)\left(x+4\right)}$$

Short Solution Steps

Use the distributive property to multiply 9 by x-9.

$$\frac{x+9x-81-5x\left(2x-9\right)}{-5x\left(x+4\right)\left(x-9\right)}$$

Combine x and 9x to get 10x.

$$\frac{10x-81-5x\left(2x-9\right)}{-5x\left(x+4\right)\left(x-9\right)}$$

Use the distributive property to multiply -5x by 2x-9.

$$\frac{10x-81-10x^{2}+45x}{-5x\left(x+4\right)\left(x-9\right)}$$

Combine 10x and 45x to get 55x.

$$\frac{55x-81-10x^{2}}{-5x\left(x+4\right)\left(x-9\right)}$$

Use the distributive property to multiply -5x by x+4.

$$\frac{55x-81-10x^{2}}{\left(-5x^{2}-20x\right)\left(x-9\right)}$$

Apply the distributive property by multiplying each term of -5x^{2}-20x by each term of x-9.

$$\frac{55x-81-10x^{2}}{-5x^{3}+45x^{2}-20x^{2}+180x}$$

Combine 45x^{2} and -20x^{2} to get 25x^{2}.

$$\frac{55x-81-10x^{2}}{-5x^{3}+25x^{2}+180x}$$

Expand

$$\frac{10x^{2}-55x+81}{5x\left(x-9\right)\left(x+4\right)}$$

Short Solution Steps

Use the distributive property to multiply 9 by x-9.

$$\frac{x+9x-81-5x\left(2x-9\right)}{-5x\left(x+4\right)\left(x-9\right)}$$

Combine x and 9x to get 10x.

$$\frac{10x-81-5x\left(2x-9\right)}{-5x\left(x+4\right)\left(x-9\right)}$$

Use the distributive property to multiply -5x by 2x-9.

$$\frac{10x-81-10x^{2}+45x}{-5x\left(x+4\right)\left(x-9\right)}$$

Combine 10x and 45x to get 55x.

$$\frac{55x-81-10x^{2}}{-5x\left(x+4\right)\left(x-9\right)}$$

Use the distributive property to multiply -5x by x+4.

$$\frac{55x-81-10x^{2}}{\left(-5x^{2}-20x\right)\left(x-9\right)}$$

Apply the distributive property by multiplying each term of -5x^{2}-20x by each term of x-9.

$$\frac{55x-81-10x^{2}}{-5x^{3}+45x^{2}-20x^{2}+180x}$$

Combine 45x^{2} and -20x^{2} to get 25x^{2}.

$$\frac{55x-81-10x^{2}}{-5x^{3}+25x^{2}+180x}$$