Solve 1p+8/p^2+1p-2-3/p+2

$$\frac { 1 p + 8 } { p ^ { 2 } + 1 p - 2 } - \frac { 3 } { p + 2 }$$

Evaluate

$$-\frac{2p-11}{\left(p-1\right)\left(p+2\right)}$$

Short Solution Steps

Factor p^{2}+1p-2.

$$\frac{1p+8}{\left(p-1\right)\left(p+2\right)}-\frac{3}{p+2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(p-1\right)\left(p+2\right) and p+2 is \left(p-1\right)\left(p+2\right). Multiply \frac{3}{p+2} times \frac{p-1}{p-1}.

$$\frac{1p+8}{\left(p-1\right)\left(p+2\right)}-\frac{3\left(p-1\right)}{\left(p-1\right)\left(p+2\right)}$$

Since \frac{1p+8}{\left(p-1\right)\left(p+2\right)} and \frac{3\left(p-1\right)}{\left(p-1\right)\left(p+2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1p+8-3\left(p-1\right)}{\left(p-1\right)\left(p+2\right)}$$

Do the multiplications in 1p+8-3\left(p-1\right).

$$\frac{p+8-3p+3}{\left(p-1\right)\left(p+2\right)}$$

Combine like terms in p+8-3p+3.

$$\frac{-2p+11}{\left(p-1\right)\left(p+2\right)}$$

Expand \left(p-1\right)\left(p+2\right).

$$\frac{-2p+11}{p^{2}+p-2}$$

Expand

$$\frac{11-2p}{\left(p-1\right)\left(p+2\right)}$$

Short Solution Steps

Factor p^{2}+1p-2.

$$\frac{1p+8}{\left(p-1\right)\left(p+2\right)}-\frac{3}{p+2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(p-1\right)\left(p+2\right) and p+2 is \left(p-1\right)\left(p+2\right). Multiply \frac{3}{p+2} times \frac{p-1}{p-1}.

$$\frac{1p+8}{\left(p-1\right)\left(p+2\right)}-\frac{3\left(p-1\right)}{\left(p-1\right)\left(p+2\right)}$$

Since \frac{1p+8}{\left(p-1\right)\left(p+2\right)} and \frac{3\left(p-1\right)}{\left(p-1\right)\left(p+2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1p+8-3\left(p-1\right)}{\left(p-1\right)\left(p+2\right)}$$

Do the multiplications in 1p+8-3\left(p-1\right).

$$\frac{p+8-3p+3}{\left(p-1\right)\left(p+2\right)}$$

Combine like terms in p+8-3p+3.

$$\frac{-2p+11}{\left(p-1\right)\left(p+2\right)}$$

Expand \left(p-1\right)\left(p+2\right).

$$\frac{-2p+11}{p^{2}+p-2}$$