Solve 4x+7/3x-2-5/2

$$\frac { 4 x + 7 } { 3 x - 2 } - \frac { 5 } { 2 }$$

Evaluate

$$\frac{24-7x}{2\left(3x-2\right)}$$

Short Solution Steps

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

$$\frac{2\left(4x+7\right)}{2\left(3x-2\right)}-\frac{5\left(3x-2\right)}{2\left(3x-2\right)}$$

Since \frac{2\left(4x+7\right)}{2\left(3x-2\right)} and \frac{5\left(3x-2\right)}{2\left(3x-2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(4x+7\right)-5\left(3x-2\right)}{2\left(3x-2\right)}$$

Do the multiplications in 2\left(4x+7\right)-5\left(3x-2\right).

$$\frac{8x+14-15x+10}{2\left(3x-2\right)}$$

Combine like terms in 8x+14-15x+10.

$$\frac{-7x+24}{2\left(3x-2\right)}$$

Expand 2\left(3x-2\right).

$$\frac{-7x+24}{6x-4}$$

Expand

$$-\frac{7x-24}{2\left(3x-2\right)}$$

Short Solution Steps

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

$$\frac{2\left(4x+7\right)}{2\left(3x-2\right)}-\frac{5\left(3x-2\right)}{2\left(3x-2\right)}$$

Since \frac{2\left(4x+7\right)}{2\left(3x-2\right)} and \frac{5\left(3x-2\right)}{2\left(3x-2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(4x+7\right)-5\left(3x-2\right)}{2\left(3x-2\right)}$$

Do the multiplications in 2\left(4x+7\right)-5\left(3x-2\right).

$$\frac{8x+14-15x+10}{2\left(3x-2\right)}$$

Combine like terms in 8x+14-15x+10.

$$\frac{-7x+24}{2\left(3x-2\right)}$$

Expand 2\left(3x-2\right).

$$\frac{-7x+24}{6x-4}$$