Solve x^2+3x+2/2x-3-x+1/8x-12

$$\frac{ { x }^{ 2 } +3x+2 }{ 2x-3 } - \frac{ x+1 }{ 8x-12 }$$

Evaluate

$$\frac{\left(x+1\right)\left(4x+7\right)}{4\left(2x-3\right)}$$

Short Solution Steps

Factor 8x-12.

$$\frac{x^{2}+3x+2}{2x-3}-\frac{x+1}{4\left(2x-3\right)}$$

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

$$\frac{4\left(x^{2}+3x+2\right)}{4\left(2x-3\right)}-\frac{x+1}{4\left(2x-3\right)}$$

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

$$\frac{4\left(x^{2}+3x+2\right)-\left(x+1\right)}{4\left(2x-3\right)}$$

Do the multiplications in 4\left(x^{2}+3x+2\right)-\left(x+1\right).

$$\frac{4x^{2}+12x+8-x-1}{4\left(2x-3\right)}$$

Combine like terms in 4x^{2}+12x+8-x-1.

$$\frac{4x^{2}+11x+7}{4\left(2x-3\right)}$$

Expand 4\left(2x-3\right).

$$\frac{4x^{2}+11x+7}{8x-12}$$

Expand

$$\frac{4x^{2}+11x+7}{4\left(2x-3\right)}$$

Short Solution Steps

Factor 8x-12.

$$\frac{x^{2}+3x+2}{2x-3}-\frac{x+1}{4\left(2x-3\right)}$$

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

$$\frac{4\left(x^{2}+3x+2\right)}{4\left(2x-3\right)}-\frac{x+1}{4\left(2x-3\right)}$$

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

$$\frac{4\left(x^{2}+3x+2\right)-\left(x+1\right)}{4\left(2x-3\right)}$$

Do the multiplications in 4\left(x^{2}+3x+2\right)-\left(x+1\right).

$$\frac{4x^{2}+12x+8-x-1}{4\left(2x-3\right)}$$

Combine like terms in 4x^{2}+12x+8-x-1.

$$\frac{4x^{2}+11x+7}{4\left(2x-3\right)}$$

Expand 4\left(2x-3\right).

$$\frac{4x^{2}+11x+7}{8x-12}$$