Solve 2/5ax+1/2ax+1/10ax+1/2aax=

$$\frac { 2 } { 5 } a x + \frac { 1 } { 2 } a x + \frac { 1 } { 10 } a x + \frac { 1 } { 2 a } a x =$$

Evaluate

$$ax+\frac{x}{2}$$

Solution Steps

Combine \frac{2}{5}ax and \frac{1}{2}ax to get \frac{9}{10}ax.

$$\frac{9}{10}ax+\frac{1}{10}ax+\frac{1}{2a}ax$$

Combine \frac{9}{10}ax and \frac{1}{10}ax to get ax.

$$ax+\frac{1}{2a}ax$$

Express \frac{1}{2a}a as a single fraction.

$$ax+\frac{a}{2a}x$$

Cancel out a in both numerator and denominator.

$$ax+\frac{1}{2}x$$

Express \frac{1}{2}x as a single fraction.

$$ax+\frac{x}{2}$$

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

$$\frac{2ax}{2}+\frac{x}{2}$$

Since \frac{2ax}{2} and \frac{x}{2} have the same denominator, add them by adding their numerators.

$$\frac{2ax+x}{2}$$

Factor

$$\frac{x\left(2a+1\right)}{2}$$

Solution Steps

Combine \frac{2}{5}ax and \frac{1}{2}ax to get \frac{9}{10}ax.

$$factor(\frac{9}{10}ax+\frac{1}{10}ax+\frac{1}{2a}ax)$$

Combine \frac{9}{10}ax and \frac{1}{10}ax to get ax.

$$factor(ax+\frac{1}{2a}ax)$$

Express \frac{1}{2a}a as a single fraction.

$$factor(ax+\frac{a}{2a}x)$$

Cancel out a in both numerator and denominator.

$$factor(ax+\frac{1}{2}x)$$

Express \frac{1}{2}x as a single fraction.

$$factor(ax+\frac{x}{2})$$

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

$$factor(\frac{2ax}{2}+\frac{x}{2})$$

Since \frac{2ax}{2} and \frac{x}{2} have the same denominator, add them by adding their numerators.

$$factor(\frac{2ax+x}{2})$$

Consider 2ax+x. Factor out x.

$$x\left(2a+1\right)$$

Rewrite the complete factored expression.

$$\frac{x\left(2a+1\right)}{2}$$