Solve 7a/4a-8-a-7/a-2

$$\frac { 7 a } { 4 a - 8 } - \frac { a - 7 } { a - 2 }$$

Evaluate

$$\frac{3a+28}{4\left(a-2\right)}$$

Short Solution Steps

Factor 4a-8.

$$\frac{7a}{4\left(a-2\right)}-\frac{a-7}{a-2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4\left(a-2\right) and a-2 is 4\left(a-2\right). Multiply \frac{a-7}{a-2} times \frac{4}{4}.

$$\frac{7a}{4\left(a-2\right)}-\frac{4\left(a-7\right)}{4\left(a-2\right)}$$

Since \frac{7a}{4\left(a-2\right)} and \frac{4\left(a-7\right)}{4\left(a-2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7a-4\left(a-7\right)}{4\left(a-2\right)}$$

Do the multiplications in 7a-4\left(a-7\right).

$$\frac{7a-4a+28}{4\left(a-2\right)}$$

Combine like terms in 7a-4a+28.

$$\frac{3a+28}{4\left(a-2\right)}$$

Expand 4\left(a-2\right).

$$\frac{3a+28}{4a-8}$$

Expand

$$\frac{3a+28}{4\left(a-2\right)}$$

Short Solution Steps

Factor 4a-8.

$$\frac{7a}{4\left(a-2\right)}-\frac{a-7}{a-2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4\left(a-2\right) and a-2 is 4\left(a-2\right). Multiply \frac{a-7}{a-2} times \frac{4}{4}.

$$\frac{7a}{4\left(a-2\right)}-\frac{4\left(a-7\right)}{4\left(a-2\right)}$$

Since \frac{7a}{4\left(a-2\right)} and \frac{4\left(a-7\right)}{4\left(a-2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7a-4\left(a-7\right)}{4\left(a-2\right)}$$

Do the multiplications in 7a-4\left(a-7\right).

$$\frac{7a-4a+28}{4\left(a-2\right)}$$

Combine like terms in 7a-4a+28.

$$\frac{3a+28}{4\left(a-2\right)}$$

Expand 4\left(a-2\right).

$$\frac{3a+28}{4a-8}$$