Solve 4/3x-1/x^2/frac{2{3x^2}+1/x}

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

Evaluate

$$\frac{4x-3}{3x+2}$$

Solution Steps

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

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

Since \frac{4x}{3x^{2}} and \frac{3}{3x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Since \frac{2}{3x^{2}} and \frac{3x}{3x^{2}} have the same denominator, add them by adding their numerators.

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

Divide \frac{4x-3}{3x^{2}} by \frac{2+3x}{3x^{2}} by multiplying \frac{4x-3}{3x^{2}} by the reciprocal of \frac{2+3x}{3x^{2}}.

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

Cancel out 3x^{2} in both numerator and denominator.

$$\frac{4x-3}{3x+2}$$

Expand

$$\frac{4x-3}{3x+2}$$

Solution Steps

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

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

Since \frac{4x}{3x^{2}} and \frac{3}{3x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Since \frac{2}{3x^{2}} and \frac{3x}{3x^{2}} have the same denominator, add them by adding their numerators.

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

Divide \frac{4x-3}{3x^{2}} by \frac{2+3x}{3x^{2}} by multiplying \frac{4x-3}{3x^{2}} by the reciprocal of \frac{2+3x}{3x^{2}}.

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

Cancel out 3x^{2} in both numerator and denominator.

$$\frac{4x-3}{3x+2}$$