Solve 20p+8/(p-8)(p-1)*p-8/18p+72=

$$\frac { 20 p + 8 } { ( p - 8 ) ( p - 1 ) } \cdot \frac { p - 8 } { 18 p + 72 } =$$

Evaluate

$$\frac{2\left(5p+2\right)}{9\left(p-1\right)\left(p+4\right)}$$

Short Solution Steps

Apply the distributive property by multiplying each term of p-8 by each term of p-1.

$$\frac{20p+8}{p^{2}-p-8p+8}\times \frac{p-8}{18p+72}$$

Combine -p and -8p to get -9p.

$$\frac{20p+8}{p^{2}-9p+8}\times \frac{p-8}{18p+72}$$

Multiply \frac{20p+8}{p^{2}-9p+8} times \frac{p-8}{18p+72} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(20p+8\right)\left(p-8\right)}{\left(p^{2}-9p+8\right)\left(18p+72\right)}$$

Factor the expressions that are not already factored.

$$\frac{4\left(p-8\right)\left(5p+2\right)}{18\left(p-8\right)\left(p-1\right)\left(p+4\right)}$$

Cancel out 2\left(p-8\right) in both numerator and denominator.

$$\frac{2\left(5p+2\right)}{9\left(p-1\right)\left(p+4\right)}$$

Expand the expression.

$$\frac{10p+4}{9p^{2}+27p-36}$$

Expand

$$\frac{2\left(5p+2\right)}{9\left(p-1\right)\left(p+4\right)}$$

Short Solution Steps

Apply the distributive property by multiplying each term of p-8 by each term of p-1.

$$\frac{20p+8}{p^{2}-p-8p+8}\times \frac{p-8}{18p+72}$$

Combine -p and -8p to get -9p.

$$\frac{20p+8}{p^{2}-9p+8}\times \frac{p-8}{18p+72}$$

Multiply \frac{20p+8}{p^{2}-9p+8} times \frac{p-8}{18p+72} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(20p+8\right)\left(p-8\right)}{\left(p^{2}-9p+8\right)\left(18p+72\right)}$$

Factor the expressions that are not already factored.

$$\frac{4\left(p-8\right)\left(5p+2\right)}{18\left(p-8\right)\left(p-1\right)\left(p+4\right)}$$

Cancel out 2\left(p-8\right) in both numerator and denominator.

$$\frac{2\left(5p+2\right)}{9\left(p-1\right)\left(p+4\right)}$$

Expand the expression.

$$\frac{10p+4}{9p^{2}+27p-36}$$