Solve 17b^2+3/b-8+13b^2-10/8-b

$$\frac { 17 b ^ { 2 } + 3 } { b - 8 } + \frac { 13 b ^ { 2 } - 10 } { 8 - b }$$

Evaluate

$$\frac{4b^{2}+13}{b-8}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b-8 and 8-b is b-8. Multiply \frac{13b^{2}-10}{8-b} times \frac{-1}{-1}.

$$\frac{17b^{2}+3}{b-8}+\frac{-\left(13b^{2}-10\right)}{b-8}$$

Since \frac{17b^{2}+3}{b-8} and \frac{-\left(13b^{2}-10\right)}{b-8} have the same denominator, add them by adding their numerators.

$$\frac{17b^{2}+3-\left(13b^{2}-10\right)}{b-8}$$

Do the multiplications in 17b^{2}+3-\left(13b^{2}-10\right).

$$\frac{17b^{2}+3-13b^{2}+10}{b-8}$$

Combine like terms in 17b^{2}+3-13b^{2}+10.

$$\frac{4b^{2}+13}{b-8}$$

Expand

$$\frac{4b^{2}+13}{b-8}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b-8 and 8-b is b-8. Multiply \frac{13b^{2}-10}{8-b} times \frac{-1}{-1}.

$$\frac{17b^{2}+3}{b-8}+\frac{-\left(13b^{2}-10\right)}{b-8}$$

Since \frac{17b^{2}+3}{b-8} and \frac{-\left(13b^{2}-10\right)}{b-8} have the same denominator, add them by adding their numerators.

$$\frac{17b^{2}+3-\left(13b^{2}-10\right)}{b-8}$$

Do the multiplications in 17b^{2}+3-\left(13b^{2}-10\right).

$$\frac{17b^{2}+3-13b^{2}+10}{b-8}$$

Combine like terms in 17b^{2}+3-13b^{2}+10.

$$\frac{4b^{2}+13}{b-8}$$