Solve 1/4x+7x/frac{1{6}-3/2x}

$$\frac { \frac { 1 } { 4 x } + 7 x } { \frac { 1 } { 6 } - \frac { 3 } { 2 x } }$$

Evaluate

$$\frac{3\left(28x^{2}+1\right)}{2\left(x-9\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 7x times \frac{4x}{4x}.

$$\frac{\frac{1}{4x}+\frac{7x\times 4x}{4x}}{\frac{1}{6}-\frac{3}{2x}}$$

Since \frac{1}{4x} and \frac{7x\times 4x}{4x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1+7x\times 4x}{4x}}{\frac{1}{6}-\frac{3}{2x}}$$

Do the multiplications in 1+7x\times 4x.

$$\frac{\frac{1+28x^{2}}{4x}}{\frac{1}{6}-\frac{3}{2x}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 2x is 6x. Multiply \frac{1}{6} times \frac{x}{x}. Multiply \frac{3}{2x} times \frac{3}{3}.

$$\frac{\frac{1+28x^{2}}{4x}}{\frac{x}{6x}-\frac{3\times 3}{6x}}$$

Since \frac{x}{6x} and \frac{3\times 3}{6x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1+28x^{2}}{4x}}{\frac{x-3\times 3}{6x}}$$

Do the multiplications in x-3\times 3.

$$\frac{\frac{1+28x^{2}}{4x}}{\frac{x-9}{6x}}$$

Divide \frac{1+28x^{2}}{4x} by \frac{x-9}{6x} by multiplying \frac{1+28x^{2}}{4x} by the reciprocal of \frac{x-9}{6x}.

$$\frac{\left(1+28x^{2}\right)\times 6x}{4x\left(x-9\right)}$$

Cancel out 2x in both numerator and denominator.

$$\frac{3\left(28x^{2}+1\right)}{2\left(x-9\right)}$$

Use the distributive property to multiply 3 by 28x^{2}+1.

$$\frac{84x^{2}+3}{2\left(x-9\right)}$$

Use the distributive property to multiply 2 by x-9.

$$\frac{84x^{2}+3}{2x-18}$$

Expand

$$\frac{3\left(28x^{2}+1\right)}{2\left(x-9\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 7x times \frac{4x}{4x}.

$$\frac{\frac{1}{4x}+\frac{7x\times 4x}{4x}}{\frac{1}{6}-\frac{3}{2x}}$$

Since \frac{1}{4x} and \frac{7x\times 4x}{4x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1+7x\times 4x}{4x}}{\frac{1}{6}-\frac{3}{2x}}$$

Do the multiplications in 1+7x\times 4x.

$$\frac{\frac{1+28x^{2}}{4x}}{\frac{1}{6}-\frac{3}{2x}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 2x is 6x. Multiply \frac{1}{6} times \frac{x}{x}. Multiply \frac{3}{2x} times \frac{3}{3}.

$$\frac{\frac{1+28x^{2}}{4x}}{\frac{x}{6x}-\frac{3\times 3}{6x}}$$

Since \frac{x}{6x} and \frac{3\times 3}{6x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1+28x^{2}}{4x}}{\frac{x-3\times 3}{6x}}$$

Do the multiplications in x-3\times 3.

$$\frac{\frac{1+28x^{2}}{4x}}{\frac{x-9}{6x}}$$

Divide \frac{1+28x^{2}}{4x} by \frac{x-9}{6x} by multiplying \frac{1+28x^{2}}{4x} by the reciprocal of \frac{x-9}{6x}.

$$\frac{\left(1+28x^{2}\right)\times 6x}{4x\left(x-9\right)}$$

Cancel out 2x in both numerator and denominator.

$$\frac{3\left(28x^{2}+1\right)}{2\left(x-9\right)}$$

Use the distributive property to multiply 3 by 28x^{2}+1.

$$\frac{84x^{2}+3}{2\left(x-9\right)}$$

Use the distributive property to multiply 2 by x-9.

$$\frac{84x^{2}+3}{2x-18}$$