Solve 24/5/x-2+41/5/x+3

$$\frac { 2 \frac { 4 } { 5 } } { x - 2 } + \frac { 4 \frac { 1 } { 5 } } { x + 3 }$$

Evaluate

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

Short Solution Steps

Express \frac{\frac{2\times 5+4}{5}}{x-2} as a single fraction.

$$\frac{2\times 5+4}{5\left(x-2\right)}+\frac{\frac{4\times 5+1}{5}}{x+3}$$

Multiply 2 and 5 to get 10.

$$\frac{10+4}{5\left(x-2\right)}+\frac{\frac{4\times 5+1}{5}}{x+3}$$

Add 10 and 4 to get 14.

$$\frac{14}{5\left(x-2\right)}+\frac{\frac{4\times 5+1}{5}}{x+3}$$

Express \frac{\frac{4\times 5+1}{5}}{x+3} as a single fraction.

$$\frac{14}{5\left(x-2\right)}+\frac{4\times 5+1}{5\left(x+3\right)}$$

Multiply 4 and 5 to get 20.

$$\frac{14}{5\left(x-2\right)}+\frac{20+1}{5\left(x+3\right)}$$

Add 20 and 1 to get 21.

$$\frac{14}{5\left(x-2\right)}+\frac{21}{5\left(x+3\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5\left(x-2\right) and 5\left(x+3\right) is 5\left(x-2\right)\left(x+3\right). Multiply \frac{14}{5\left(x-2\right)} times \frac{x+3}{x+3}. Multiply \frac{21}{5\left(x+3\right)} times \frac{x-2}{x-2}.

$$\frac{14\left(x+3\right)}{5\left(x-2\right)\left(x+3\right)}+\frac{21\left(x-2\right)}{5\left(x-2\right)\left(x+3\right)}$$

Since \frac{14\left(x+3\right)}{5\left(x-2\right)\left(x+3\right)} and \frac{21\left(x-2\right)}{5\left(x-2\right)\left(x+3\right)} have the same denominator, add them by adding their numerators.

$$\frac{14\left(x+3\right)+21\left(x-2\right)}{5\left(x-2\right)\left(x+3\right)}$$

Do the multiplications in 14\left(x+3\right)+21\left(x-2\right).

$$\frac{14x+42+21x-42}{5\left(x-2\right)\left(x+3\right)}$$

Combine like terms in 14x+42+21x-42.

$$\frac{35x}{5\left(x-2\right)\left(x+3\right)}$$

Cancel out 5 in both numerator and denominator.

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

Expand \left(x-2\right)\left(x+3\right).

$$\frac{7x}{x^{2}+x-6}$$

Expand

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

Short Solution Steps

Express \frac{\frac{2\times 5+4}{5}}{x-2} as a single fraction.

$$\frac{2\times 5+4}{5\left(x-2\right)}+\frac{\frac{4\times 5+1}{5}}{x+3}$$

Multiply 2 and 5 to get 10.

$$\frac{10+4}{5\left(x-2\right)}+\frac{\frac{4\times 5+1}{5}}{x+3}$$

Add 10 and 4 to get 14.

$$\frac{14}{5\left(x-2\right)}+\frac{\frac{4\times 5+1}{5}}{x+3}$$

Express \frac{\frac{4\times 5+1}{5}}{x+3} as a single fraction.

$$\frac{14}{5\left(x-2\right)}+\frac{4\times 5+1}{5\left(x+3\right)}$$

Multiply 4 and 5 to get 20.

$$\frac{14}{5\left(x-2\right)}+\frac{20+1}{5\left(x+3\right)}$$

Add 20 and 1 to get 21.

$$\frac{14}{5\left(x-2\right)}+\frac{21}{5\left(x+3\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5\left(x-2\right) and 5\left(x+3\right) is 5\left(x-2\right)\left(x+3\right). Multiply \frac{14}{5\left(x-2\right)} times \frac{x+3}{x+3}. Multiply \frac{21}{5\left(x+3\right)} times \frac{x-2}{x-2}.

$$\frac{14\left(x+3\right)}{5\left(x-2\right)\left(x+3\right)}+\frac{21\left(x-2\right)}{5\left(x-2\right)\left(x+3\right)}$$

Since \frac{14\left(x+3\right)}{5\left(x-2\right)\left(x+3\right)} and \frac{21\left(x-2\right)}{5\left(x-2\right)\left(x+3\right)} have the same denominator, add them by adding their numerators.

$$\frac{14\left(x+3\right)+21\left(x-2\right)}{5\left(x-2\right)\left(x+3\right)}$$

Do the multiplications in 14\left(x+3\right)+21\left(x-2\right).

$$\frac{14x+42+21x-42}{5\left(x-2\right)\left(x+3\right)}$$

Combine like terms in 14x+42+21x-42.

$$\frac{35x}{5\left(x-2\right)\left(x+3\right)}$$

Cancel out 5 in both numerator and denominator.

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

Expand \left(x-2\right)\left(x+3\right).

$$\frac{7x}{x^{2}+x-6}$$