Solve 25-4/5x/frac{4{25x}-5}

$$\frac { 25 - \frac { 4 } { 5 x } } { \frac { 4 } { 25 x } - 5 }$$

Evaluate

$$-5$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 25 times \frac{5x}{5x}.

$$\frac{\frac{25\times 5x}{5x}-\frac{4}{5x}}{\frac{4}{25x}-5}$$

Since \frac{25\times 5x}{5x} and \frac{4}{5x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{25\times 5x-4}{5x}}{\frac{4}{25x}-5}$$

Do the multiplications in 25\times 5x-4.

$$\frac{\frac{125x-4}{5x}}{\frac{4}{25x}-5}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{25x}{25x}.

$$\frac{\frac{125x-4}{5x}}{\frac{4}{25x}-\frac{5\times 25x}{25x}}$$

Since \frac{4}{25x} and \frac{5\times 25x}{25x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{125x-4}{5x}}{\frac{4-5\times 25x}{25x}}$$

Do the multiplications in 4-5\times 25x.

$$\frac{\frac{125x-4}{5x}}{\frac{4-125x}{25x}}$$

Divide \frac{125x-4}{5x} by \frac{4-125x}{25x} by multiplying \frac{125x-4}{5x} by the reciprocal of \frac{4-125x}{25x}.

$$\frac{\left(125x-4\right)\times 25x}{5x\left(4-125x\right)}$$

Extract the negative sign in 125x-4.

$$\frac{-25x\left(-125x+4\right)}{5x\left(-125x+4\right)}$$

Cancel out 5x\left(-125x+4\right) in both numerator and denominator.

$$-5$$

Factor

$$-5$$