Solve 8/5(3x+2)-7/3(3x+2)

$$\frac { 8 } { 5 ( 3 x + 2 ) } - \frac { 7 } { 3 ( 3 x + 2 ) }$$

Evaluate

$$-\frac{11}{15\left(3x+2\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5\left(3x+2\right) and 3\left(3x+2\right) is 15\left(3x+2\right). Multiply \frac{8}{5\left(3x+2\right)} times \frac{3}{3}. Multiply \frac{7}{3\left(3x+2\right)} times \frac{5}{5}.

$$\frac{8\times 3}{15\left(3x+2\right)}-\frac{7\times 5}{15\left(3x+2\right)}$$

Since \frac{8\times 3}{15\left(3x+2\right)} and \frac{7\times 5}{15\left(3x+2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8\times 3-7\times 5}{15\left(3x+2\right)}$$

Do the multiplications in 8\times 3-7\times 5.

$$\frac{24-35}{15\left(3x+2\right)}$$

Do the calculations in 24-35.

$$\frac{-11}{15\left(3x+2\right)}$$

Expand 15\left(3x+2\right).

$$\frac{-11}{45x+30}$$

Expand

$$-\frac{11}{15\left(3x+2\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5\left(3x+2\right) and 3\left(3x+2\right) is 15\left(3x+2\right). Multiply \frac{8}{5\left(3x+2\right)} times \frac{3}{3}. Multiply \frac{7}{3\left(3x+2\right)} times \frac{5}{5}.

$$\frac{8\times 3}{15\left(3x+2\right)}-\frac{7\times 5}{15\left(3x+2\right)}$$

Since \frac{8\times 3}{15\left(3x+2\right)} and \frac{7\times 5}{15\left(3x+2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8\times 3-7\times 5}{15\left(3x+2\right)}$$

Do the multiplications in 8\times 3-7\times 5.

$$\frac{24-35}{15\left(3x+2\right)}$$

Do the calculations in 24-35.

$$\frac{-11}{15\left(3x+2\right)}$$

Expand 15\left(3x+2\right).

$$\frac{-11}{45x+30}$$