Solve 11+3/x-2/2x-3

$$\frac { 11 + \frac { 3 } { x - 2 } } { 2 x - 3 }$$

Evaluate

$$\frac{11x-19}{\left(x-2\right)\left(2x-3\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 11 times \frac{x-2}{x-2}.

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

Since \frac{11\left(x-2\right)}{x-2} and \frac{3}{x-2} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 11\left(x-2\right)+3.

$$\frac{\frac{11x-22+3}{x-2}}{2x-3}$$

Combine like terms in 11x-22+3.

$$\frac{\frac{11x-19}{x-2}}{2x-3}$$

Express \frac{\frac{11x-19}{x-2}}{2x-3} as a single fraction.

$$\frac{11x-19}{\left(x-2\right)\left(2x-3\right)}$$

Apply the distributive property by multiplying each term of x-2 by each term of 2x-3.

$$\frac{11x-19}{2x^{2}-3x-4x+6}$$

Combine -3x and -4x to get -7x.

$$\frac{11x-19}{2x^{2}-7x+6}$$

Expand

$$\frac{11x-19}{\left(x-2\right)\left(2x-3\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 11 times \frac{x-2}{x-2}.

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

Since \frac{11\left(x-2\right)}{x-2} and \frac{3}{x-2} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 11\left(x-2\right)+3.

$$\frac{\frac{11x-22+3}{x-2}}{2x-3}$$

Combine like terms in 11x-22+3.

$$\frac{\frac{11x-19}{x-2}}{2x-3}$$

Express \frac{\frac{11x-19}{x-2}}{2x-3} as a single fraction.

$$\frac{11x-19}{\left(x-2\right)\left(2x-3\right)}$$

Apply the distributive property by multiplying each term of x-2 by each term of 2x-3.

$$\frac{11x-19}{2x^{2}-3x-4x+6}$$

Combine -3x and -4x to get -7x.

$$\frac{11x-19}{2x^{2}-7x+6}$$