Solve 6x+5/x-5-1/3x+20+2

$$\frac { \frac { 6 x + 5 } { x - 5 } - 1 } { 3 x + 20 + 2 }$$

Evaluate

$$\frac{5\left(x+2\right)}{\left(x-5\right)\left(3x+22\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x-5}{x-5}.

$$\frac{\frac{6x+5}{x-5}-\frac{x-5}{x-5}}{3x+20+2}$$

Since \frac{6x+5}{x-5} and \frac{x-5}{x-5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{6x+5-\left(x-5\right)}{x-5}}{3x+20+2}$$

Do the multiplications in 6x+5-\left(x-5\right).

$$\frac{\frac{6x+5-x+5}{x-5}}{3x+20+2}$$

Combine like terms in 6x+5-x+5.

$$\frac{\frac{5x+10}{x-5}}{3x+20+2}$$

Add 20 and 2 to get 22.

$$\frac{\frac{5x+10}{x-5}}{3x+22}$$

Express \frac{\frac{5x+10}{x-5}}{3x+22} as a single fraction.

$$\frac{5x+10}{\left(x-5\right)\left(3x+22\right)}$$

Apply the distributive property by multiplying each term of x-5 by each term of 3x+22.

$$\frac{5x+10}{3x^{2}+22x-15x-110}$$

Combine 22x and -15x to get 7x.

$$\frac{5x+10}{3x^{2}+7x-110}$$

Expand

$$\frac{5\left(x+2\right)}{\left(x-5\right)\left(3x+22\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x-5}{x-5}.

$$\frac{\frac{6x+5}{x-5}-\frac{x-5}{x-5}}{3x+20+2}$$

Since \frac{6x+5}{x-5} and \frac{x-5}{x-5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{6x+5-\left(x-5\right)}{x-5}}{3x+20+2}$$

Do the multiplications in 6x+5-\left(x-5\right).

$$\frac{\frac{6x+5-x+5}{x-5}}{3x+20+2}$$

Combine like terms in 6x+5-x+5.

$$\frac{\frac{5x+10}{x-5}}{3x+20+2}$$

Add 20 and 2 to get 22.

$$\frac{\frac{5x+10}{x-5}}{3x+22}$$

Express \frac{\frac{5x+10}{x-5}}{3x+22} as a single fraction.

$$\frac{5x+10}{\left(x-5\right)\left(3x+22\right)}$$

Apply the distributive property by multiplying each term of x-5 by each term of 3x+22.

$$\frac{5x+10}{3x^{2}+22x-15x-110}$$

Combine 22x and -15x to get 7x.

$$\frac{5x+10}{3x^{2}+7x-110}$$