Solve 6x/3x-1+4x/2x+5

$$\frac { 6 x } { 3 x - 1 } + \frac { 4 x } { 2 x + 5 }$$

Evaluate

$$\frac{2x\left(12x+13\right)}{\left(3x-1\right)\left(2x+5\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x-1 and 2x+5 is \left(3x-1\right)\left(2x+5\right). Multiply \frac{6x}{3x-1} times \frac{2x+5}{2x+5}. Multiply \frac{4x}{2x+5} times \frac{3x-1}{3x-1}.

$$\frac{6x\left(2x+5\right)}{\left(3x-1\right)\left(2x+5\right)}+\frac{4x\left(3x-1\right)}{\left(3x-1\right)\left(2x+5\right)}$$

Since \frac{6x\left(2x+5\right)}{\left(3x-1\right)\left(2x+5\right)} and \frac{4x\left(3x-1\right)}{\left(3x-1\right)\left(2x+5\right)} have the same denominator, add them by adding their numerators.

$$\frac{6x\left(2x+5\right)+4x\left(3x-1\right)}{\left(3x-1\right)\left(2x+5\right)}$$

Do the multiplications in 6x\left(2x+5\right)+4x\left(3x-1\right).

$$\frac{12x^{2}+30x+12x^{2}-4x}{\left(3x-1\right)\left(2x+5\right)}$$

Combine like terms in 12x^{2}+30x+12x^{2}-4x.

$$\frac{24x^{2}+26x}{\left(3x-1\right)\left(2x+5\right)}$$

Expand \left(3x-1\right)\left(2x+5\right).

$$\frac{24x^{2}+26x}{6x^{2}+13x-5}$$

Factor

$$\frac{2x\left(12x+13\right)}{\left(3x-1\right)\left(2x+5\right)}$$