Solve x:2x+3:7:5

$$x : 2 x + 3 : 7 : 5$$

Evaluate

$$\frac{x^{2}}{2}+\frac{3}{35}$$

Short Solution Steps

Express \frac{x}{2}x as a single fraction.

$$\frac{xx}{2}+\frac{\frac{3}{7}}{5}$$

Express \frac{\frac{3}{7}}{5} as a single fraction.

$$\frac{xx}{2}+\frac{3}{7\times 5}$$

Multiply 7 and 5 to get 35.

$$\frac{xx}{2}+\frac{3}{35}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 35 is 70. Multiply \frac{xx}{2} times \frac{35}{35}. Multiply \frac{3}{35} times \frac{2}{2}.

$$\frac{35xx}{70}+\frac{3\times 2}{70}$$

Since \frac{35xx}{70} and \frac{3\times 2}{70} have the same denominator, add them by adding their numerators.

$$\frac{35xx+3\times 2}{70}$$

Do the multiplications in 35xx+3\times 2.

$$\frac{35x^{2}+6}{70}$$

Factor

$$\frac{35x^{2}+6}{70}$$

Solution Steps

Factor out \frac{1}{70}. Polynomial 35x^{2}+6 is not factored since it does not have any rational roots.

$$\frac{35xx+6}{70}$$