Solve 2a-3/3a+3x+2/10x+x-a/5ax=

$$\frac { 2 a - 3 } { 3 a } + \frac { 3 x + 2 } { 10 x } + \frac { x - a } { 5 a x } =$$

Evaluate

$$\frac{29}{30}-\frac{4}{5a}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3a and 10x is 30ax. Multiply \frac{2a-3}{3a} times \frac{10x}{10x}. Multiply \frac{3x+2}{10x} times \frac{3a}{3a}.

$$\frac{\left(2a-3\right)\times 10x}{30ax}+\frac{\left(3x+2\right)\times 3a}{30ax}+\frac{x-a}{5ax}$$

Since \frac{\left(2a-3\right)\times 10x}{30ax} and \frac{\left(3x+2\right)\times 3a}{30ax} have the same denominator, add them by adding their numerators.

$$\frac{\left(2a-3\right)\times 10x+\left(3x+2\right)\times 3a}{30ax}+\frac{x-a}{5ax}$$

Do the multiplications in \left(2a-3\right)\times 10x+\left(3x+2\right)\times 3a.

$$\frac{20ax-30x+9xa+6a}{30ax}+\frac{x-a}{5ax}$$

Combine like terms in 20ax-30x+9xa+6a.

$$\frac{29ax-30x+6a}{30ax}+\frac{x-a}{5ax}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 30ax and 5ax is 30ax. Multiply \frac{x-a}{5ax} times \frac{6}{6}.

$$\frac{29ax-30x+6a}{30ax}+\frac{6\left(x-a\right)}{30ax}$$

Since \frac{29ax-30x+6a}{30ax} and \frac{6\left(x-a\right)}{30ax} have the same denominator, add them by adding their numerators.

$$\frac{29ax-30x+6a+6\left(x-a\right)}{30ax}$$

Do the multiplications in 29ax-30x+6a+6\left(x-a\right).

$$\frac{29ax-30x+6a+6x-6a}{30ax}$$

Combine like terms in 29ax-30x+6a+6x-6a.

$$\frac{29ax-24x}{30ax}$$

Factor the expressions that are not already factored in \frac{29ax-24x}{30ax}.

$$\frac{x\left(29a-24\right)}{30ax}$$

Cancel out x in both numerator and denominator.

$$\frac{29a-24}{30a}$$

Expand

$$\frac{29}{30}-\frac{4}{5a}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3a and 10x is 30ax. Multiply \frac{2a-3}{3a} times \frac{10x}{10x}. Multiply \frac{3x+2}{10x} times \frac{3a}{3a}.

$$\frac{\left(2a-3\right)\times 10x}{30ax}+\frac{\left(3x+2\right)\times 3a}{30ax}+\frac{x-a}{5ax}$$

Since \frac{\left(2a-3\right)\times 10x}{30ax} and \frac{\left(3x+2\right)\times 3a}{30ax} have the same denominator, add them by adding their numerators.

$$\frac{\left(2a-3\right)\times 10x+\left(3x+2\right)\times 3a}{30ax}+\frac{x-a}{5ax}$$

Do the multiplications in \left(2a-3\right)\times 10x+\left(3x+2\right)\times 3a.

$$\frac{20ax-30x+9xa+6a}{30ax}+\frac{x-a}{5ax}$$

Combine like terms in 20ax-30x+9xa+6a.

$$\frac{29ax-30x+6a}{30ax}+\frac{x-a}{5ax}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 30ax and 5ax is 30ax. Multiply \frac{x-a}{5ax} times \frac{6}{6}.

$$\frac{29ax-30x+6a}{30ax}+\frac{6\left(x-a\right)}{30ax}$$

Since \frac{29ax-30x+6a}{30ax} and \frac{6\left(x-a\right)}{30ax} have the same denominator, add them by adding their numerators.

$$\frac{29ax-30x+6a+6\left(x-a\right)}{30ax}$$

Do the multiplications in 29ax-30x+6a+6\left(x-a\right).

$$\frac{29ax-30x+6a+6x-6a}{30ax}$$

Combine like terms in 29ax-30x+6a+6x-6a.

$$\frac{29ax-24x}{30ax}$$

Factor the expressions that are not already factored in \frac{29ax-24x}{30ax}.

$$\frac{x\left(29a-24\right)}{30ax}$$

Cancel out x in both numerator and denominator.

$$\frac{29a-24}{30a}$$