Solve x^2/9-25/4/frac{4{x}-x/5}

$$\frac { \frac { x ^ { 2 } } { 9 } - \frac { 25 } { 4 } } { \frac { 4 } { x } - \frac { x } { 5 } }$$

Evaluate

$$\frac{5x\left(4x^{2}-225\right)}{36\left(20-x^{2}\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9 and 4 is 36. Multiply \frac{x^{2}}{9} times \frac{4}{4}. Multiply \frac{25}{4} times \frac{9}{9}.

$$\frac{\frac{4x^{2}}{36}-\frac{25\times 9}{36}}{\frac{4}{x}-\frac{x}{5}}$$

Since \frac{4x^{2}}{36} and \frac{25\times 9}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4x^{2}-25\times 9}{36}}{\frac{4}{x}-\frac{x}{5}}$$

Do the multiplications in 4x^{2}-25\times 9.

$$\frac{\frac{4x^{2}-225}{36}}{\frac{4}{x}-\frac{x}{5}}$$

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

$$\frac{\frac{4x^{2}-225}{36}}{\frac{4\times 5}{5x}-\frac{xx}{5x}}$$

Since \frac{4\times 5}{5x} and \frac{xx}{5x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4x^{2}-225}{36}}{\frac{4\times 5-xx}{5x}}$$

Do the multiplications in 4\times 5-xx.

$$\frac{\frac{4x^{2}-225}{36}}{\frac{20-x^{2}}{5x}}$$

Divide \frac{4x^{2}-225}{36} by \frac{20-x^{2}}{5x} by multiplying \frac{4x^{2}-225}{36} by the reciprocal of \frac{20-x^{2}}{5x}.

$$\frac{\left(4x^{2}-225\right)\times 5x}{36\left(20-x^{2}\right)}$$

Use the distributive property to multiply 4x^{2}-225 by 5.

$$\frac{\left(20x^{2}-1125\right)x}{36\left(20-x^{2}\right)}$$

Use the distributive property to multiply 20x^{2}-1125 by x.

$$\frac{20x^{3}-1125x}{36\left(20-x^{2}\right)}$$

Use the distributive property to multiply 36 by 20-x^{2}.

$$\frac{20x^{3}-1125x}{720-36x^{2}}$$

Expand

$$-\frac{5\left(4x^{3}-225x\right)}{36\left(x^{2}-20\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9 and 4 is 36. Multiply \frac{x^{2}}{9} times \frac{4}{4}. Multiply \frac{25}{4} times \frac{9}{9}.

$$\frac{\frac{4x^{2}}{36}-\frac{25\times 9}{36}}{\frac{4}{x}-\frac{x}{5}}$$

Since \frac{4x^{2}}{36} and \frac{25\times 9}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4x^{2}-25\times 9}{36}}{\frac{4}{x}-\frac{x}{5}}$$

Do the multiplications in 4x^{2}-25\times 9.

$$\frac{\frac{4x^{2}-225}{36}}{\frac{4}{x}-\frac{x}{5}}$$

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

$$\frac{\frac{4x^{2}-225}{36}}{\frac{4\times 5}{5x}-\frac{xx}{5x}}$$

Since \frac{4\times 5}{5x} and \frac{xx}{5x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4x^{2}-225}{36}}{\frac{4\times 5-xx}{5x}}$$

Do the multiplications in 4\times 5-xx.

$$\frac{\frac{4x^{2}-225}{36}}{\frac{20-x^{2}}{5x}}$$

Divide \frac{4x^{2}-225}{36} by \frac{20-x^{2}}{5x} by multiplying \frac{4x^{2}-225}{36} by the reciprocal of \frac{20-x^{2}}{5x}.

$$\frac{\left(4x^{2}-225\right)\times 5x}{36\left(20-x^{2}\right)}$$

Use the distributive property to multiply 4x^{2}-225 by 5.

$$\frac{\left(20x^{2}-1125\right)x}{36\left(20-x^{2}\right)}$$

Use the distributive property to multiply 20x^{2}-1125 by x.

$$\frac{20x^{3}-1125x}{36\left(20-x^{2}\right)}$$

Use the distributive property to multiply 36 by 20-x^{2}.

$$\frac{20x^{3}-1125x}{720-36x^{2}}$$