Solve 7/x-4+5x/(x-4)^2=

$$\frac { 7 } { x - 4 } + \frac { 5 x } { ( x - 4 ) ^ { 2 } } =$$

Evaluate

$$\frac{4\left(3x-7\right)}{\left(x-4\right)^{2}}$$

Short Solution Steps

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

$$\frac{7\left(x-4\right)}{\left(x-4\right)^{2}}+\frac{5x}{\left(x-4\right)^{2}}$$

Since \frac{7\left(x-4\right)}{\left(x-4\right)^{2}} and \frac{5x}{\left(x-4\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{7\left(x-4\right)+5x}{\left(x-4\right)^{2}}$$

Do the multiplications in 7\left(x-4\right)+5x.

$$\frac{7x-28+5x}{\left(x-4\right)^{2}}$$

Combine like terms in 7x-28+5x.

$$\frac{12x-28}{\left(x-4\right)^{2}}$$

Expand \left(x-4\right)^{2}.

$$\frac{12x-28}{x^{2}-8x+16}$$

Expand

$$\frac{4\left(3x-7\right)}{\left(x-4\right)^{2}}$$

Short Solution Steps

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

$$\frac{7\left(x-4\right)}{\left(x-4\right)^{2}}+\frac{5x}{\left(x-4\right)^{2}}$$

Since \frac{7\left(x-4\right)}{\left(x-4\right)^{2}} and \frac{5x}{\left(x-4\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{7\left(x-4\right)+5x}{\left(x-4\right)^{2}}$$

Do the multiplications in 7\left(x-4\right)+5x.

$$\frac{7x-28+5x}{\left(x-4\right)^{2}}$$

Combine like terms in 7x-28+5x.

$$\frac{12x-28}{\left(x-4\right)^{2}}$$

Expand \left(x-4\right)^{2}.

$$\frac{12x-28}{x^{2}-8x+16}$$