Solve 6x/2(3x^2+2)+1/4(x+2)

$$\frac { 6 x } { 2 ( 3 x ^ { 2 } + 2 ) } + \frac { 1 } { 4 ( x + 2 ) }$$

Evaluate

$$\frac{15x^{2}+24x+2}{4\left(x+2\right)\left(3x^{2}+2\right)}$$

Short Solution Steps

Cancel out 2 in both numerator and denominator.

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

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

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

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

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

Do the multiplications in 3x\times 4\left(x+2\right)+3x^{2}+2.

$$\frac{12x^{2}+24x+3x^{2}+2}{4\left(x+2\right)\left(3x^{2}+2\right)}$$

Combine like terms in 12x^{2}+24x+3x^{2}+2.

$$\frac{15x^{2}+24x+2}{4\left(x+2\right)\left(3x^{2}+2\right)}$$

Expand 4\left(x+2\right)\left(3x^{2}+2\right).

$$\frac{15x^{2}+24x+2}{12x^{3}+24x^{2}+8x+16}$$

Expand

$$\frac{15x^{2}+24x+2}{4\left(x+2\right)\left(3x^{2}+2\right)}$$

Short Solution Steps

Cancel out 2 in both numerator and denominator.

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

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

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

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

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

Do the multiplications in 3x\times 4\left(x+2\right)+3x^{2}+2.

$$\frac{12x^{2}+24x+3x^{2}+2}{4\left(x+2\right)\left(3x^{2}+2\right)}$$

Combine like terms in 12x^{2}+24x+3x^{2}+2.

$$\frac{15x^{2}+24x+2}{4\left(x+2\right)\left(3x^{2}+2\right)}$$

Expand 4\left(x+2\right)\left(3x^{2}+2\right).

$$\frac{15x^{2}+24x+2}{12x^{3}+24x^{2}+8x+16}$$