Solve x+20%-10%divx=

$$x+20 \% -10 \% \div x=$$

Evaluate

$$x+\frac{1}{5}-\frac{1}{10x}$$

Short Solution Steps

Reduce the fraction \frac{20}{100} to lowest terms by extracting and canceling out 20.

$$x+\frac{1}{5}-\frac{\frac{10}{100}}{x}$$

Express \frac{\frac{10}{100}}{x} as a single fraction.

$$x+\frac{1}{5}-\frac{10}{100x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 100x is 100x. Multiply \frac{1}{5} times \frac{20x}{20x}.

$$x+\frac{20x}{100x}-\frac{10}{100x}$$

Since \frac{20x}{100x} and \frac{10}{100x} have the same denominator, subtract them by subtracting their numerators.

$$x+\frac{20x-10}{100x}$$

Factor the expressions that are not already factored in \frac{20x-10}{100x}.

$$x+\frac{10\left(2x-1\right)}{100x}$$

Cancel out 10 in both numerator and denominator.

$$x+\frac{2x-1}{10x}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{10x}{10x}.

$$\frac{x\times 10x}{10x}+\frac{2x-1}{10x}$$

Since \frac{x\times 10x}{10x} and \frac{2x-1}{10x} have the same denominator, add them by adding their numerators.

$$\frac{x\times 10x+2x-1}{10x}$$

Do the multiplications in x\times 10x+2x-1.

$$\frac{10x^{2}+2x-1}{10x}$$

Factor the expressions that are not already factored in \frac{10x^{2}+2x-1}{10x}.

$$\frac{10\left(x-\left(-\frac{1}{10}\sqrt{11}-\frac{1}{10}\right)\right)\left(x-\left(\frac{1}{10}\sqrt{11}-\frac{1}{10}\right)\right)}{10x}$$

Cancel out 10 in both numerator and denominator.

$$\frac{\left(x-\left(-\frac{1}{10}\sqrt{11}-\frac{1}{10}\right)\right)\left(x-\left(\frac{1}{10}\sqrt{11}-\frac{1}{10}\right)\right)}{x}$$

To find the opposite of -\frac{1}{10}\sqrt{11}-\frac{1}{10}, find the opposite of each term.

$$\frac{\left(x-\left(-\frac{1}{10}\sqrt{11}\right)-\left(-\frac{1}{10}\right)\right)\left(x-\left(\frac{1}{10}\sqrt{11}-\frac{1}{10}\right)\right)}{x}$$

The opposite of -\frac{1}{10}\sqrt{11} is \frac{1}{10}\sqrt{11}.

$$\frac{\left(x+\frac{1}{10}\sqrt{11}-\left(-\frac{1}{10}\right)\right)\left(x-\left(\frac{1}{10}\sqrt{11}-\frac{1}{10}\right)\right)}{x}$$

The opposite of -\frac{1}{10} is \frac{1}{10}.

$$\frac{\left(x+\frac{1}{10}\sqrt{11}+\frac{1}{10}\right)\left(x-\left(\frac{1}{10}\sqrt{11}-\frac{1}{10}\right)\right)}{x}$$

To find the opposite of \frac{1}{10}\sqrt{11}-\frac{1}{10}, find the opposite of each term.

$$\frac{\left(x+\frac{1}{10}\sqrt{11}+\frac{1}{10}\right)\left(x-\frac{1}{10}\sqrt{11}-\left(-\frac{1}{10}\right)\right)}{x}$$

The opposite of -\frac{1}{10} is \frac{1}{10}.

$$\frac{\left(x+\frac{1}{10}\sqrt{11}+\frac{1}{10}\right)\left(x-\frac{1}{10}\sqrt{11}+\frac{1}{10}\right)}{x}$$

Apply the distributive property by multiplying each term of x+\frac{1}{10}\sqrt{11}+\frac{1}{10} by each term of x-\frac{1}{10}\sqrt{11}+\frac{1}{10}.

$$\frac{x^{2}+x\left(-\frac{1}{10}\right)\sqrt{11}+x\times \frac{1}{10}+\frac{1}{10}\sqrt{11}x+\frac{1}{10}\sqrt{11}\left(-\frac{1}{10}\right)\sqrt{11}+\frac{1}{10}\sqrt{11}\times \frac{1}{10}+\frac{1}{10}x+\frac{1}{10}\left(-\frac{1}{10}\right)\sqrt{11}+\frac{1}{10}\times \frac{1}{10}}{x}$$

Multiply \sqrt{11} and \sqrt{11} to get 11.

$$\frac{x^{2}+x\left(-\frac{1}{10}\right)\sqrt{11}+x\times \frac{1}{10}+\frac{1}{10}\sqrt{11}x+\frac{1}{10}\times 11\left(-\frac{1}{10}\right)+\frac{1}{10}\sqrt{11}\times \frac{1}{10}+\frac{1}{10}x+\frac{1}{10}\left(-\frac{1}{10}\right)\sqrt{11}+\frac{1}{10}\times \frac{1}{10}}{x}$$

Combine x\left(-\frac{1}{10}\right)\sqrt{11} and \frac{1}{10}\sqrt{11}x to get 0.

$$\frac{x^{2}+x\times \frac{1}{10}+\frac{1}{10}\times 11\left(-\frac{1}{10}\right)+\frac{1}{10}\sqrt{11}\times \frac{1}{10}+\frac{1}{10}x+\frac{1}{10}\left(-\frac{1}{10}\right)\sqrt{11}+\frac{1}{10}\times \frac{1}{10}}{x}$$

Multiply \frac{1}{10} and 11 to get \frac{11}{10}.

$$\frac{x^{2}+x\times \frac{1}{10}+\frac{11}{10}\left(-\frac{1}{10}\right)+\frac{1}{10}\sqrt{11}\times \frac{1}{10}+\frac{1}{10}x+\frac{1}{10}\left(-\frac{1}{10}\right)\sqrt{11}+\frac{1}{10}\times \frac{1}{10}}{x}$$

Multiply \frac{11}{10} times -\frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x^{2}+x\times \frac{1}{10}+\frac{11\left(-1\right)}{10\times 10}+\frac{1}{10}\sqrt{11}\times \frac{1}{10}+\frac{1}{10}x+\frac{1}{10}\left(-\frac{1}{10}\right)\sqrt{11}+\frac{1}{10}\times \frac{1}{10}}{x}$$

Do the multiplications in the fraction \frac{11\left(-1\right)}{10\times 10}.

$$\frac{x^{2}+x\times \frac{1}{10}+\frac{-11}{100}+\frac{1}{10}\sqrt{11}\times \frac{1}{10}+\frac{1}{10}x+\frac{1}{10}\left(-\frac{1}{10}\right)\sqrt{11}+\frac{1}{10}\times \frac{1}{10}}{x}$$

Fraction \frac{-11}{100} can be rewritten as -\frac{11}{100} by extracting the negative sign.

$$\frac{x^{2}+x\times \frac{1}{10}-\frac{11}{100}+\frac{1}{10}\sqrt{11}\times \frac{1}{10}+\frac{1}{10}x+\frac{1}{10}\left(-\frac{1}{10}\right)\sqrt{11}+\frac{1}{10}\times \frac{1}{10}}{x}$$

Multiply \frac{1}{10} times \frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x^{2}+x\times \frac{1}{10}-\frac{11}{100}+\frac{1\times 1}{10\times 10}\sqrt{11}+\frac{1}{10}x+\frac{1}{10}\left(-\frac{1}{10}\right)\sqrt{11}+\frac{1}{10}\times \frac{1}{10}}{x}$$

Do the multiplications in the fraction \frac{1\times 1}{10\times 10}.

$$\frac{x^{2}+x\times \frac{1}{10}-\frac{11}{100}+\frac{1}{100}\sqrt{11}+\frac{1}{10}x+\frac{1}{10}\left(-\frac{1}{10}\right)\sqrt{11}+\frac{1}{10}\times \frac{1}{10}}{x}$$

Combine x\times \frac{1}{10} and \frac{1}{10}x to get \frac{1}{5}x.

$$\frac{x^{2}+\frac{1}{5}x-\frac{11}{100}+\frac{1}{100}\sqrt{11}+\frac{1}{10}\left(-\frac{1}{10}\right)\sqrt{11}+\frac{1}{10}\times \frac{1}{10}}{x}$$

Multiply \frac{1}{10} times -\frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x^{2}+\frac{1}{5}x-\frac{11}{100}+\frac{1}{100}\sqrt{11}+\frac{1\left(-1\right)}{10\times 10}\sqrt{11}+\frac{1}{10}\times \frac{1}{10}}{x}$$

Do the multiplications in the fraction \frac{1\left(-1\right)}{10\times 10}.

$$\frac{x^{2}+\frac{1}{5}x-\frac{11}{100}+\frac{1}{100}\sqrt{11}+\frac{-1}{100}\sqrt{11}+\frac{1}{10}\times \frac{1}{10}}{x}$$

Fraction \frac{-1}{100} can be rewritten as -\frac{1}{100} by extracting the negative sign.

$$\frac{x^{2}+\frac{1}{5}x-\frac{11}{100}+\frac{1}{100}\sqrt{11}-\frac{1}{100}\sqrt{11}+\frac{1}{10}\times \frac{1}{10}}{x}$$

Combine \frac{1}{100}\sqrt{11} and -\frac{1}{100}\sqrt{11} to get 0.

$$\frac{x^{2}+\frac{1}{5}x-\frac{11}{100}+\frac{1}{10}\times \frac{1}{10}}{x}$$

Multiply \frac{1}{10} times \frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x^{2}+\frac{1}{5}x-\frac{11}{100}+\frac{1\times 1}{10\times 10}}{x}$$

Do the multiplications in the fraction \frac{1\times 1}{10\times 10}.

$$\frac{x^{2}+\frac{1}{5}x-\frac{11}{100}+\frac{1}{100}}{x}$$

Since -\frac{11}{100} and \frac{1}{100} have the same denominator, add them by adding their numerators.

$$\frac{x^{2}+\frac{1}{5}x+\frac{-11+1}{100}}{x}$$

Add -11 and 1 to get -10.

$$\frac{x^{2}+\frac{1}{5}x+\frac{-10}{100}}{x}$$

Reduce the fraction \frac{-10}{100} to lowest terms by extracting and canceling out 10.

$$\frac{x^{2}+\frac{1}{5}x-\frac{1}{10}}{x}$$

Factor

$$\frac{\left(x-\frac{-\sqrt{11}-1}{10}\right)\left(x-\frac{\sqrt{11}-1}{10}\right)}{x}$$