Solve 265x/2x+3-6/2x^2+3x+2/x

$$26 \frac { 5 x } { 2 x + 3 } - \frac { 6 } { 2 x ^ { 2 } + 3 x } + \frac { 2 } { x }$$

Evaluate

$$\frac{2\left(65x+2\right)}{2x+3}$$

Short Solution Steps

Express 26\times \frac{5x}{2x+3} as a single fraction.

$$\frac{26\times 5x}{2x+3}-\frac{6}{2x^{2}+3x}+\frac{2}{x}$$

Factor 2x^{2}+3x.

$$\frac{26\times 5x}{2x+3}-\frac{6}{x\left(2x+3\right)}+\frac{2}{x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x+3 and x\left(2x+3\right) is x\left(2x+3\right). Multiply \frac{26\times 5x}{2x+3} times \frac{x}{x}.

$$\frac{26\times 5xx}{x\left(2x+3\right)}-\frac{6}{x\left(2x+3\right)}+\frac{2}{x}$$

Since \frac{26\times 5xx}{x\left(2x+3\right)} and \frac{6}{x\left(2x+3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{26\times 5xx-6}{x\left(2x+3\right)}+\frac{2}{x}$$

Do the multiplications in 26\times 5xx-6.

$$\frac{130x^{2}-6}{x\left(2x+3\right)}+\frac{2}{x}$$

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

$$\frac{130x^{2}-6}{x\left(2x+3\right)}+\frac{2\left(2x+3\right)}{x\left(2x+3\right)}$$

Since \frac{130x^{2}-6}{x\left(2x+3\right)} and \frac{2\left(2x+3\right)}{x\left(2x+3\right)} have the same denominator, add them by adding their numerators.

$$\frac{130x^{2}-6+2\left(2x+3\right)}{x\left(2x+3\right)}$$

Do the multiplications in 130x^{2}-6+2\left(2x+3\right).

$$\frac{130x^{2}-6+4x+6}{x\left(2x+3\right)}$$

Combine like terms in 130x^{2}-6+4x+6.

$$\frac{130x^{2}+4x}{x\left(2x+3\right)}$$

Factor the expressions that are not already factored in \frac{130x^{2}+4x}{x\left(2x+3\right)}.

$$\frac{2x\left(65x+2\right)}{x\left(2x+3\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{2\left(65x+2\right)}{2x+3}$$

Use the distributive property to multiply 2 by 65x+2.

$$\frac{130x+4}{2x+3}$$

Factor

$$\frac{2\left(65x+2\right)}{2x+3}$$