Solve (x+6)div(2x-7)+1divx

$$(x+6) \div (2x-7)+1 \div x$$

Evaluate

$$\frac{x^{2}+8x-7}{x\left(2x-7\right)}$$

Short Solution Steps

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

$$\frac{\left(x+6\right)x}{x\left(2x-7\right)}+\frac{2x-7}{x\left(2x-7\right)}$$

Since \frac{\left(x+6\right)x}{x\left(2x-7\right)} and \frac{2x-7}{x\left(2x-7\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(x+6\right)x+2x-7}{x\left(2x-7\right)}$$

Do the multiplications in \left(x+6\right)x+2x-7.

$$\frac{x^{2}+6x+2x-7}{x\left(2x-7\right)}$$

Combine like terms in x^{2}+6x+2x-7.

$$\frac{x^{2}+8x-7}{x\left(2x-7\right)}$$

Expand x\left(2x-7\right).

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

Expand

$$\frac{x^{2}+8x-7}{x\left(2x-7\right)}$$

Short Solution Steps

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

$$\frac{\left(x+6\right)x}{x\left(2x-7\right)}+\frac{2x-7}{x\left(2x-7\right)}$$

Since \frac{\left(x+6\right)x}{x\left(2x-7\right)} and \frac{2x-7}{x\left(2x-7\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(x+6\right)x+2x-7}{x\left(2x-7\right)}$$

Do the multiplications in \left(x+6\right)x+2x-7.

$$\frac{x^{2}+6x+2x-7}{x\left(2x-7\right)}$$

Combine like terms in x^{2}+6x+2x-7.

$$\frac{x^{2}+8x-7}{x\left(2x-7\right)}$$

Expand x\left(2x-7\right).

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