Solve 14/x-3y-24/3x-9

$$\frac { 14 } { x - 3 y } - \frac { 24 } { 3 x - 9 }$$

Evaluate

$$\frac{6\left(x+4y-7\right)}{\left(x-3\right)\left(x-3y\right)}$$

Short Solution Steps

Factor 3x-9.

$$\frac{14}{x-3y}-\frac{24}{3\left(x-3\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3y and 3\left(x-3\right) is 3\left(x-3\right)\left(x-3y\right). Multiply \frac{14}{x-3y} times \frac{3\left(x-3\right)}{3\left(x-3\right)}. Multiply \frac{24}{3\left(x-3\right)} times \frac{x-3y}{x-3y}.

$$\frac{14\times 3\left(x-3\right)}{3\left(x-3\right)\left(x-3y\right)}-\frac{24\left(x-3y\right)}{3\left(x-3\right)\left(x-3y\right)}$$

Since \frac{14\times 3\left(x-3\right)}{3\left(x-3\right)\left(x-3y\right)} and \frac{24\left(x-3y\right)}{3\left(x-3\right)\left(x-3y\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{14\times 3\left(x-3\right)-24\left(x-3y\right)}{3\left(x-3\right)\left(x-3y\right)}$$

Do the multiplications in 14\times 3\left(x-3\right)-24\left(x-3y\right).

$$\frac{42x-126-24x+72y}{3\left(x-3\right)\left(x-3y\right)}$$

Combine like terms in 42x-126-24x+72y.

$$\frac{18x-126+72y}{3\left(x-3\right)\left(x-3y\right)}$$

Factor the expressions that are not already factored in \frac{18x-126+72y}{3\left(x-3\right)\left(x-3y\right)}.

$$\frac{18\left(x+4y-7\right)}{3\left(x-3\right)\left(x-3y\right)}$$

Cancel out 3 in both numerator and denominator.

$$\frac{6\left(x+4y-7\right)}{\left(x-3\right)\left(x-3y\right)}$$

Expand \left(x-3\right)\left(x-3y\right).

$$\frac{6\left(x+4y-7\right)}{x^{2}-3xy-3x+9y}$$

Use the distributive property to multiply 6 by x+4y-7.

$$\frac{6x+24y-42}{x^{2}-3xy-3x+9y}$$

Factor

$$\frac{6\left(x+4y-7\right)}{\left(x-3\right)\left(x-3y\right)}$$