Solve 20p+8/(p-8)(p-1)*p-y/16p+72

$$\frac { 20 p + 8 } { ( p - 8 ) ( p - 1 ) } \cdot \frac { p - y } { 16 p + 72 }$$

Evaluate

$$\frac{\left(p-y\right)\left(5p+2\right)}{2\left(p-8\right)\left(p-1\right)\left(2p+9\right)}$$

Short Solution Steps

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

$$\frac{20p+8}{p^{2}-p-8p+8}\times \frac{p-y}{16p+72}$$

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

$$\frac{20p+8}{p^{2}-9p+8}\times \frac{p-y}{16p+72}$$

Multiply \frac{20p+8}{p^{2}-9p+8} times \frac{p-y}{16p+72} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(20p+8\right)\left(p-y\right)}{\left(p^{2}-9p+8\right)\left(16p+72\right)}$$

Factor the expressions that are not already factored.

$$\frac{4\left(5p+2\right)\left(-y+p\right)}{8\left(p-8\right)\left(p-1\right)\left(2p+9\right)}$$

Cancel out 4 in both numerator and denominator.

$$\frac{\left(5p+2\right)\left(-y+p\right)}{2\left(p-8\right)\left(p-1\right)\left(2p+9\right)}$$

Expand the expression.

$$\frac{-5py-2y+5p^{2}+2p}{4p^{3}-18p^{2}-130p+144}$$

Expand

$$-\frac{5py+2y-5p^{2}-2p}{2\left(p-8\right)\left(p-1\right)\left(2p+9\right)}$$

Short Solution Steps

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

$$\frac{20p+8}{p^{2}-p-8p+8}\times \frac{p-y}{16p+72}$$

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

$$\frac{20p+8}{p^{2}-9p+8}\times \frac{p-y}{16p+72}$$

Multiply \frac{20p+8}{p^{2}-9p+8} times \frac{p-y}{16p+72} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(20p+8\right)\left(p-y\right)}{\left(p^{2}-9p+8\right)\left(16p+72\right)}$$

Factor the expressions that are not already factored.

$$\frac{4\left(5p+2\right)\left(-y+p\right)}{8\left(p-8\right)\left(p-1\right)\left(2p+9\right)}$$

Cancel out 4 in both numerator and denominator.

$$\frac{\left(5p+2\right)\left(-y+p\right)}{2\left(p-8\right)\left(p-1\right)\left(2p+9\right)}$$

Expand the expression.

$$\frac{-5py-2y+5p^{2}+2p}{4p^{3}-18p^{2}-130p+144}$$