Solve 7/4(2y+1)-5/6(2y+1)

$$\frac { 7 } { 4 ( 2 y + 1 ) } - \frac { 5 } { 6 ( 2 y + 1 ) }$$

Evaluate

$$\frac{11}{12\left(2y+1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4\left(2y+1\right) and 6\left(2y+1\right) is 12\left(2y+1\right). Multiply \frac{7}{4\left(2y+1\right)} times \frac{3}{3}. Multiply \frac{5}{6\left(2y+1\right)} times \frac{2}{2}.

$$\frac{7\times 3}{12\left(2y+1\right)}-\frac{5\times 2}{12\left(2y+1\right)}$$

Since \frac{7\times 3}{12\left(2y+1\right)} and \frac{5\times 2}{12\left(2y+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7\times 3-5\times 2}{12\left(2y+1\right)}$$

Do the multiplications in 7\times 3-5\times 2.

$$\frac{21-10}{12\left(2y+1\right)}$$

Do the calculations in 21-10.

$$\frac{11}{12\left(2y+1\right)}$$

Expand 12\left(2y+1\right).

$$\frac{11}{24y+12}$$

Expand

$$\frac{11}{12\left(2y+1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4\left(2y+1\right) and 6\left(2y+1\right) is 12\left(2y+1\right). Multiply \frac{7}{4\left(2y+1\right)} times \frac{3}{3}. Multiply \frac{5}{6\left(2y+1\right)} times \frac{2}{2}.

$$\frac{7\times 3}{12\left(2y+1\right)}-\frac{5\times 2}{12\left(2y+1\right)}$$

Since \frac{7\times 3}{12\left(2y+1\right)} and \frac{5\times 2}{12\left(2y+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7\times 3-5\times 2}{12\left(2y+1\right)}$$

Do the multiplications in 7\times 3-5\times 2.

$$\frac{21-10}{12\left(2y+1\right)}$$

Do the calculations in 21-10.

$$\frac{11}{12\left(2y+1\right)}$$

Expand 12\left(2y+1\right).

$$\frac{11}{24y+12}$$