Solve 7/3x+5/4x-2/8x^2

$$\frac { 7 } { 3 x } + \frac { 5 } { 4 x } - \frac { 2 } { 8 x ^ { 2 } }$$

Evaluate

$$\frac{43x-3}{12x^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x and 4x is 12x. Multiply \frac{7}{3x} times \frac{4}{4}. Multiply \frac{5}{4x} times \frac{3}{3}.

$$\frac{7\times 4}{12x}+\frac{5\times 3}{12x}-\frac{2}{8x^{2}}$$

Since \frac{7\times 4}{12x} and \frac{5\times 3}{12x} have the same denominator, add them by adding their numerators.

$$\frac{7\times 4+5\times 3}{12x}-\frac{2}{8x^{2}}$$

Do the multiplications in 7\times 4+5\times 3.

$$\frac{28+15}{12x}-\frac{2}{8x^{2}}$$

Do the calculations in 28+15.

$$\frac{43}{12x}-\frac{2}{8x^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 12x and 8x^{2} is 24x^{2}. Multiply \frac{43}{12x} times \frac{2x}{2x}. Multiply \frac{2}{8x^{2}} times \frac{3}{3}.

$$\frac{43\times 2x}{24x^{2}}-\frac{2\times 3}{24x^{2}}$$

Since \frac{43\times 2x}{24x^{2}} and \frac{2\times 3}{24x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{43\times 2x-2\times 3}{24x^{2}}$$

Do the multiplications in 43\times 2x-2\times 3.

$$\frac{86x-6}{24x^{2}}$$

Factor the expressions that are not already factored in \frac{86x-6}{24x^{2}}.

$$\frac{2\left(43x-3\right)}{24x^{2}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{43x-3}{12x^{2}}$$

Factor

$$\frac{43x-3}{12x^{2}}$$