Solve 2/6y+2-4/18y^2+24y+6

$$\frac { 2 } { 6 y + 2 } - \frac { 4 } { 18 y ^ { 2 } + 24 y + 6 }$$

Evaluate

$$\frac{1}{3\left(y+1\right)}$$

Short Solution Steps

Factor 6y+2. Factor 18y^{2}+24y+6.

$$\frac{2}{2\left(3y+1\right)}-\frac{4}{6\left(y+1\right)\left(3y+1\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(3y+1\right) and 6\left(y+1\right)\left(3y+1\right) is 6\left(y+1\right)\left(3y+1\right). Multiply \frac{2}{2\left(3y+1\right)} times \frac{3\left(y+1\right)}{3\left(y+1\right)}.

$$\frac{2\times 3\left(y+1\right)}{6\left(y+1\right)\left(3y+1\right)}-\frac{4}{6\left(y+1\right)\left(3y+1\right)}$$

Since \frac{2\times 3\left(y+1\right)}{6\left(y+1\right)\left(3y+1\right)} and \frac{4}{6\left(y+1\right)\left(3y+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 3\left(y+1\right)-4}{6\left(y+1\right)\left(3y+1\right)}$$

Do the multiplications in 2\times 3\left(y+1\right)-4.

$$\frac{6y+6-4}{6\left(y+1\right)\left(3y+1\right)}$$

Combine like terms in 6y+6-4.

$$\frac{6y+2}{6\left(y+1\right)\left(3y+1\right)}$$

Factor the expressions that are not already factored in \frac{6y+2}{6\left(y+1\right)\left(3y+1\right)}.

$$\frac{2\left(3y+1\right)}{6\left(y+1\right)\left(3y+1\right)}$$

Cancel out 2\left(3y+1\right) in both numerator and denominator.

$$\frac{1}{3\left(y+1\right)}$$

Expand 3\left(y+1\right).

$$\frac{1}{3y+3}$$

Factor

$$\frac{1}{3\left(y+1\right)}$$