Solve 15b^2+9/b-6+1b^2-2/6-b

$$\frac { 15 b ^ { 2 } + 9 } { b - 6 } + \frac { 1 b ^ { 2 } - 2 } { 6 - b }$$

Evaluate

$$\frac{14b^{2}+11}{b-6}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b-6 and 6-b is b-6. Multiply \frac{1b^{2}-2}{6-b} times \frac{-1}{-1}.

$$\frac{15b^{2}+9}{b-6}+\frac{-\left(b^{2}-2\right)}{b-6}$$

Since \frac{15b^{2}+9}{b-6} and \frac{-\left(b^{2}-2\right)}{b-6} have the same denominator, add them by adding their numerators.

$$\frac{15b^{2}+9-\left(1b^{2}-2\right)}{b-6}$$

Do the multiplications in 15b^{2}+9-\left(1b^{2}-2\right).

$$\frac{15b^{2}+9-b^{2}+2}{b-6}$$

Combine like terms in 15b^{2}+9-b^{2}+2.

$$\frac{14b^{2}+11}{b-6}$$

Expand

$$\frac{14b^{2}+11}{b-6}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b-6 and 6-b is b-6. Multiply \frac{1b^{2}-2}{6-b} times \frac{-1}{-1}.

$$\frac{15b^{2}+9}{b-6}+\frac{-\left(b^{2}-2\right)}{b-6}$$

Since \frac{15b^{2}+9}{b-6} and \frac{-\left(b^{2}-2\right)}{b-6} have the same denominator, add them by adding their numerators.

$$\frac{15b^{2}+9-\left(1b^{2}-2\right)}{b-6}$$

Do the multiplications in 15b^{2}+9-\left(1b^{2}-2\right).

$$\frac{15b^{2}+9-b^{2}+2}{b-6}$$

Combine like terms in 15b^{2}+9-b^{2}+2.

$$\frac{14b^{2}+11}{b-6}$$