Solve x^2/8+x/15+4/49

$$\frac{ { x }^{ 2 } }{ 8 } + \frac{ x }{ 15 } + \frac{ 4 }{ 49 }$$

Evaluate

$$\frac{x^{2}}{8}+\frac{x}{15}+\frac{4}{49}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8 and 15 is 120. Multiply \frac{x^{2}}{8} times \frac{15}{15}. Multiply \frac{x}{15} times \frac{8}{8}.

$$\frac{15x^{2}}{120}+\frac{8x}{120}+\frac{4}{49}$$

Since \frac{15x^{2}}{120} and \frac{8x}{120} have the same denominator, add them by adding their numerators.

$$\frac{15x^{2}+8x}{120}+\frac{4}{49}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 120 and 49 is 5880. Multiply \frac{15x^{2}+8x}{120} times \frac{49}{49}. Multiply \frac{4}{49} times \frac{120}{120}.

$$\frac{49\left(15x^{2}+8x\right)}{5880}+\frac{4\times 120}{5880}$$

Since \frac{49\left(15x^{2}+8x\right)}{5880} and \frac{4\times 120}{5880} have the same denominator, add them by adding their numerators.

$$\frac{49\left(15x^{2}+8x\right)+4\times 120}{5880}$$

Do the multiplications in 49\left(15x^{2}+8x\right)+4\times 120.

$$\frac{735x^{2}+392x+480}{5880}$$

Factor

$$\frac{735x^{2}+392x+480}{5880}$$

Solution Steps

Factor out \frac{1}{5880}. Polynomial 735x^{2}+392x+480 is not factored since it does not have any rational roots.

$$\frac{735x^{2}+392x+480}{5880}$$