Solve 10/b-1-4/b+8

$$\frac { 10 } { b - 1 } - \frac { 4 } { b + 8 }$$

Evaluate

$$\frac{6\left(b+14\right)}{\left(b-1\right)\left(b+8\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b-1 and b+8 is \left(b-1\right)\left(b+8\right). Multiply \frac{10}{b-1} times \frac{b+8}{b+8}. Multiply \frac{4}{b+8} times \frac{b-1}{b-1}.

$$\frac{10\left(b+8\right)}{\left(b-1\right)\left(b+8\right)}-\frac{4\left(b-1\right)}{\left(b-1\right)\left(b+8\right)}$$

Since \frac{10\left(b+8\right)}{\left(b-1\right)\left(b+8\right)} and \frac{4\left(b-1\right)}{\left(b-1\right)\left(b+8\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10\left(b+8\right)-4\left(b-1\right)}{\left(b-1\right)\left(b+8\right)}$$

Do the multiplications in 10\left(b+8\right)-4\left(b-1\right).

$$\frac{10b+80-4b+4}{\left(b-1\right)\left(b+8\right)}$$

Combine like terms in 10b+80-4b+4.

$$\frac{6b+84}{\left(b-1\right)\left(b+8\right)}$$

Expand \left(b-1\right)\left(b+8\right).

$$\frac{6b+84}{b^{2}+7b-8}$$

Factor

$$\frac{6\left(b+14\right)}{\left(b-1\right)\left(b+8\right)}$$