Solve 1/5(x-90+3600/x)(100/x)=

$$\frac { 1 } { 5 } ( x - 90 + \frac { 3600 } { x } ) ( \frac { 100 } { x } ) =$$

Evaluate

$$20-\frac{1800}{x}+\frac{72000}{x^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x-90 times \frac{x}{x}.

$$\frac{1}{5}\left(\frac{\left(x-90\right)x}{x}+\frac{3600}{x}\right)\times \frac{100}{x}$$

Since \frac{\left(x-90\right)x}{x} and \frac{3600}{x} have the same denominator, add them by adding their numerators.

$$\frac{1}{5}\times \frac{\left(x-90\right)x+3600}{x}\times \frac{100}{x}$$

Do the multiplications in \left(x-90\right)x+3600.

$$\frac{1}{5}\times \frac{x^{2}-90x+3600}{x}\times \frac{100}{x}$$

Multiply \frac{1}{5} times \frac{x^{2}-90x+3600}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x^{2}-90x+3600}{5x}\times \frac{100}{x}$$

Multiply \frac{x^{2}-90x+3600}{5x} times \frac{100}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}-90x+3600\right)\times 100}{5xx}$$

Cancel out 5 in both numerator and denominator.

$$\frac{20\left(x^{2}-90x+3600\right)}{xx}$$

Multiply x and x to get x^{2}.

$$\frac{20\left(x^{2}-90x+3600\right)}{x^{2}}$$

Use the distributive property to multiply 20 by x^{2}-90x+3600.

$$\frac{20x^{2}-1800x+72000}{x^{2}}$$

Expand

$$20-\frac{1800}{x}+\frac{72000}{x^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x-90 times \frac{x}{x}.

$$\frac{1}{5}\left(\frac{\left(x-90\right)x}{x}+\frac{3600}{x}\right)\times \frac{100}{x}$$

Since \frac{\left(x-90\right)x}{x} and \frac{3600}{x} have the same denominator, add them by adding their numerators.

$$\frac{1}{5}\times \frac{\left(x-90\right)x+3600}{x}\times \frac{100}{x}$$

Do the multiplications in \left(x-90\right)x+3600.

$$\frac{1}{5}\times \frac{x^{2}-90x+3600}{x}\times \frac{100}{x}$$

Multiply \frac{1}{5} times \frac{x^{2}-90x+3600}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x^{2}-90x+3600}{5x}\times \frac{100}{x}$$

Multiply \frac{x^{2}-90x+3600}{5x} times \frac{100}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}-90x+3600\right)\times 100}{5xx}$$

Cancel out 5 in both numerator and denominator.

$$\frac{20\left(x^{2}-90x+3600\right)}{xx}$$

Multiply x and x to get x^{2}.

$$\frac{20\left(x^{2}-90x+3600\right)}{x^{2}}$$

Use the distributive property to multiply 20 by x^{2}-90x+3600.

$$\frac{20x^{2}-1800x+72000}{x^{2}}$$