Solve x=10+1/frac{1{15}+1/10+x}

$$x = 10 + \frac { 1 } { \frac { 1 } { 15 } + \frac { 1 } { 10 + x } }$$

Solve for x

$$x=-20$$

$$x=20$$

Steps Using Difference of Squares

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 15 and 10+x is 15\left(x+10\right). Multiply \frac{1}{15} times \frac{x+10}{x+10}. Multiply \frac{1}{10+x} times \frac{15}{15}.

$$x=10+\frac{1}{\frac{x+10}{15\left(x+10\right)}+\frac{15}{15\left(x+10\right)}}$$

Since \frac{x+10}{15\left(x+10\right)} and \frac{15}{15\left(x+10\right)} have the same denominator, add them by adding their numerators.

$$x=10+\frac{1}{\frac{x+10+15}{15\left(x+10\right)}}$$

Combine like terms in x+10+15.

$$x=10+\frac{1}{\frac{x+25}{15\left(x+10\right)}}$$

Variable x cannot be equal to -10 since division by zero is not defined. Divide 1 by \frac{x+25}{15\left(x+10\right)} by multiplying 1 by the reciprocal of \frac{x+25}{15\left(x+10\right)}.

$$x=10+\frac{15\left(x+10\right)}{x+25}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 10 times \frac{x+25}{x+25}.

$$x=\frac{10\left(x+25\right)}{x+25}+\frac{15\left(x+10\right)}{x+25}$$

Since \frac{10\left(x+25\right)}{x+25} and \frac{15\left(x+10\right)}{x+25} have the same denominator, add them by adding their numerators.

$$x=\frac{10\left(x+25\right)+15\left(x+10\right)}{x+25}$$

Do the multiplications in 10\left(x+25\right)+15\left(x+10\right).

$$x=\frac{10x+250+15x+150}{x+25}$$

Combine like terms in 10x+250+15x+150.

$$x=\frac{25x+400}{x+25}$$

Subtract \frac{25x+400}{x+25} from both sides.

$$x-\frac{25x+400}{x+25}=0$$

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

$$\frac{x\left(x+25\right)}{x+25}-\frac{25x+400}{x+25}=0$$

Since \frac{x\left(x+25\right)}{x+25} and \frac{25x+400}{x+25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x\left(x+25\right)-\left(25x+400\right)}{x+25}=0$$

Do the multiplications in x\left(x+25\right)-\left(25x+400\right).

$$\frac{x^{2}+25x-25x-400}{x+25}=0$$

Combine like terms in x^{2}+25x-25x-400.

$$\frac{x^{2}-400}{x+25}=0$$

Variable x cannot be equal to -25 since division by zero is not defined. Multiply both sides of the equation by x+25.

$$x^{2}-400=0$$

Consider x^{2}-400. Rewrite x^{2}-400 as x^{2}-20^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-20\right)\left(x+20\right)=0$$

To find equation solutions, solve x-20=0 and x+20=0.

$$x=20 x=-20$$

Steps by Finding Square Root

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 15 and 10+x is 15\left(x+10\right). Multiply \frac{1}{15} times \frac{x+10}{x+10}. Multiply \frac{1}{10+x} times \frac{15}{15}.

$$x=10+\frac{1}{\frac{x+10}{15\left(x+10\right)}+\frac{15}{15\left(x+10\right)}}$$

Since \frac{x+10}{15\left(x+10\right)} and \frac{15}{15\left(x+10\right)} have the same denominator, add them by adding their numerators.

$$x=10+\frac{1}{\frac{x+10+15}{15\left(x+10\right)}}$$

Combine like terms in x+10+15.

$$x=10+\frac{1}{\frac{x+25}{15\left(x+10\right)}}$$

Variable x cannot be equal to -10 since division by zero is not defined. Divide 1 by \frac{x+25}{15\left(x+10\right)} by multiplying 1 by the reciprocal of \frac{x+25}{15\left(x+10\right)}.

$$x=10+\frac{15\left(x+10\right)}{x+25}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 10 times \frac{x+25}{x+25}.

$$x=\frac{10\left(x+25\right)}{x+25}+\frac{15\left(x+10\right)}{x+25}$$

Since \frac{10\left(x+25\right)}{x+25} and \frac{15\left(x+10\right)}{x+25} have the same denominator, add them by adding their numerators.

$$x=\frac{10\left(x+25\right)+15\left(x+10\right)}{x+25}$$

Do the multiplications in 10\left(x+25\right)+15\left(x+10\right).

$$x=\frac{10x+250+15x+150}{x+25}$$

Combine like terms in 10x+250+15x+150.

$$x=\frac{25x+400}{x+25}$$

Subtract \frac{25x+400}{x+25} from both sides.

$$x-\frac{25x+400}{x+25}=0$$

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

$$\frac{x\left(x+25\right)}{x+25}-\frac{25x+400}{x+25}=0$$

Since \frac{x\left(x+25\right)}{x+25} and \frac{25x+400}{x+25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x\left(x+25\right)-\left(25x+400\right)}{x+25}=0$$

Do the multiplications in x\left(x+25\right)-\left(25x+400\right).

$$\frac{x^{2}+25x-25x-400}{x+25}=0$$

Combine like terms in x^{2}+25x-25x-400.

$$\frac{x^{2}-400}{x+25}=0$$

Variable x cannot be equal to -25 since division by zero is not defined. Multiply both sides of the equation by x+25.

$$x^{2}-400=0$$

Add 400 to both sides. Anything plus zero gives itself.

$$x^{2}=400$$

Take the square root of both sides of the equation.

$$x=20 x=-20$$

Steps Using the Quadratic Formula

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 15 and 10+x is 15\left(x+10\right). Multiply \frac{1}{15} times \frac{x+10}{x+10}. Multiply \frac{1}{10+x} times \frac{15}{15}.

$$x=10+\frac{1}{\frac{x+10}{15\left(x+10\right)}+\frac{15}{15\left(x+10\right)}}$$

Since \frac{x+10}{15\left(x+10\right)} and \frac{15}{15\left(x+10\right)} have the same denominator, add them by adding their numerators.

$$x=10+\frac{1}{\frac{x+10+15}{15\left(x+10\right)}}$$

Combine like terms in x+10+15.

$$x=10+\frac{1}{\frac{x+25}{15\left(x+10\right)}}$$

Variable x cannot be equal to -10 since division by zero is not defined. Divide 1 by \frac{x+25}{15\left(x+10\right)} by multiplying 1 by the reciprocal of \frac{x+25}{15\left(x+10\right)}.

$$x=10+\frac{15\left(x+10\right)}{x+25}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 10 times \frac{x+25}{x+25}.

$$x=\frac{10\left(x+25\right)}{x+25}+\frac{15\left(x+10\right)}{x+25}$$

Since \frac{10\left(x+25\right)}{x+25} and \frac{15\left(x+10\right)}{x+25} have the same denominator, add them by adding their numerators.

$$x=\frac{10\left(x+25\right)+15\left(x+10\right)}{x+25}$$

Do the multiplications in 10\left(x+25\right)+15\left(x+10\right).

$$x=\frac{10x+250+15x+150}{x+25}$$

Combine like terms in 10x+250+15x+150.

$$x=\frac{25x+400}{x+25}$$

Subtract \frac{25x+400}{x+25} from both sides.

$$x-\frac{25x+400}{x+25}=0$$

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

$$\frac{x\left(x+25\right)}{x+25}-\frac{25x+400}{x+25}=0$$

Since \frac{x\left(x+25\right)}{x+25} and \frac{25x+400}{x+25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x\left(x+25\right)-\left(25x+400\right)}{x+25}=0$$

Do the multiplications in x\left(x+25\right)-\left(25x+400\right).

$$\frac{x^{2}+25x-25x-400}{x+25}=0$$

Combine like terms in x^{2}+25x-25x-400.

$$\frac{x^{2}-400}{x+25}=0$$

Variable x cannot be equal to -25 since division by zero is not defined. Multiply both sides of the equation by x+25.

$$x^{2}-400=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -400 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-400\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-400\right)}}{2}$$

Multiply -4 times -400.

$$x=\frac{0±\sqrt{1600}}{2}$$

Take the square root of 1600.

$$x=\frac{0±40}{2}$$

Now solve the equation x=\frac{0±40}{2} when ± is plus. Divide 40 by 2.

$$x=20$$

Now solve the equation x=\frac{0±40}{2} when ± is minus. Divide -40 by 2.

$$x=-20$$

The equation is now solved.

$$x=20 x=-20$$