Solve 6b/6b^2+10b-4b/3b

$$\frac { 6 b } { 6 b ^ { 2 } + 10 b } - \frac { 4 b } { 3 b }$$

Evaluate

$$-\frac{12b+11}{3\left(3b+5\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{6b}{6b^{2}+10b}.

$$\frac{6b}{2b\left(3b+5\right)}-\frac{4b}{3b}$$

Cancel out 2b in both numerator and denominator.

$$\frac{3}{3b+5}-\frac{4b}{3b}$$

Cancel out b in both numerator and denominator.

$$\frac{3}{3b+5}-\frac{4}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3b+5 and 3 is 3\left(3b+5\right). Multiply \frac{3}{3b+5} times \frac{3}{3}. Multiply \frac{4}{3} times \frac{3b+5}{3b+5}.

$$\frac{3\times 3}{3\left(3b+5\right)}-\frac{4\left(3b+5\right)}{3\left(3b+5\right)}$$

Since \frac{3\times 3}{3\left(3b+5\right)} and \frac{4\left(3b+5\right)}{3\left(3b+5\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\times 3-4\left(3b+5\right)}{3\left(3b+5\right)}$$

Do the multiplications in 3\times 3-4\left(3b+5\right).

$$\frac{9-12b-20}{3\left(3b+5\right)}$$

Combine like terms in 9-12b-20.

$$\frac{-11-12b}{3\left(3b+5\right)}$$

Expand 3\left(3b+5\right).

$$\frac{-11-12b}{9b+15}$$

Factor

$$-\frac{12b+11}{3\left(3b+5\right)}$$