Solve 6+((x+5)divx^2+3x-10/x-1

$$6+((x+5) \div \frac{ { x }^{ 2 } +3x-10 }{ x-1 }$$

Evaluate

$$\frac{7x-13}{x-2}$$

Short Solution Steps

Divide x+5 by \frac{x^{2}+3x-10}{x-1} by multiplying x+5 by the reciprocal of \frac{x^{2}+3x-10}{x-1}.

$$6+\frac{\left(x+5\right)\left(x-1\right)}{x^{2}+3x-10}$$

Factor the expressions that are not already factored in \frac{\left(x+5\right)\left(x-1\right)}{x^{2}+3x-10}.

$$6+\frac{\left(x-1\right)\left(x+5\right)}{\left(x-2\right)\left(x+5\right)}$$

Cancel out x+5 in both numerator and denominator.

$$6+\frac{x-1}{x-2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{x-2}{x-2}.

$$\frac{6\left(x-2\right)}{x-2}+\frac{x-1}{x-2}$$

Since \frac{6\left(x-2\right)}{x-2} and \frac{x-1}{x-2} have the same denominator, add them by adding their numerators.

$$\frac{6\left(x-2\right)+x-1}{x-2}$$

Do the multiplications in 6\left(x-2\right)+x-1.

$$\frac{6x-12+x-1}{x-2}$$

Combine like terms in 6x-12+x-1.

$$\frac{7x-13}{x-2}$$

Expand

$$\frac{7x-13}{x-2}$$

Short Solution Steps

Divide x+5 by \frac{x^{2}+3x-10}{x-1} by multiplying x+5 by the reciprocal of \frac{x^{2}+3x-10}{x-1}.

$$6+\frac{\left(x+5\right)\left(x-1\right)}{x^{2}+3x-10}$$

Factor the expressions that are not already factored in \frac{\left(x+5\right)\left(x-1\right)}{x^{2}+3x-10}.

$$6+\frac{\left(x-1\right)\left(x+5\right)}{\left(x-2\right)\left(x+5\right)}$$

Cancel out x+5 in both numerator and denominator.

$$6+\frac{x-1}{x-2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{x-2}{x-2}.

$$\frac{6\left(x-2\right)}{x-2}+\frac{x-1}{x-2}$$

Since \frac{6\left(x-2\right)}{x-2} and \frac{x-1}{x-2} have the same denominator, add them by adding their numerators.

$$\frac{6\left(x-2\right)+x-1}{x-2}$$

Do the multiplications in 6\left(x-2\right)+x-1.

$$\frac{6x-12+x-1}{x-2}$$

Combine like terms in 6x-12+x-1.

$$\frac{7x-13}{x-2}$$