Solve x+15/x-sqrt{81}=frac{sqrt{144}+1,4}{sqrt{81}-sqrt{0,16}}

$$\frac { x + 15 } { x - \sqrt { 81 } } = \frac { \sqrt { 144 } + 1,4 } { \sqrt { 81 } - \sqrt { 0,16 } }$$

Solve for x

$$x=52$$

Steps for Solving Linear Equation

Calculate the square root of 81 and get 9.

$$\frac{x+15}{x-9}=\frac{\sqrt{144}+1,4}{\sqrt{81}-\sqrt{0,16}}$$

Calculate the square root of 144 and get 12.

$$\frac{x+15}{x-9}=\frac{12+1,4}{\sqrt{81}-\sqrt{0,16}}$$

Add 12 and 1,4 to get 13,4.

$$\frac{x+15}{x-9}=\frac{13,4}{\sqrt{81}-\sqrt{0,16}}$$

Calculate the square root of 81 and get 9.

$$\frac{x+15}{x-9}=\frac{13,4}{9-\sqrt{0,16}}$$

Calculate the square root of 0,16 and get 0,4.

$$\frac{x+15}{x-9}=\frac{13,4}{9-0,4}$$

Subtract 0,4 from 9 to get 8,6.

$$\frac{x+15}{x-9}=\frac{13,4}{8,6}$$

Expand \frac{13,4}{8,6} by multiplying both numerator and the denominator by 10.

$$\frac{x+15}{x-9}=\frac{134}{86}$$

Reduce the fraction \frac{134}{86} to lowest terms by extracting and canceling out 2.

$$\frac{x+15}{x-9}=\frac{67}{43}$$

Variable x cannot be equal to 9 since division by zero is not defined. Multiply both sides of the equation by 43\left(x-9\right), the least common multiple of x-9;43.

$$43\left(x+15\right)=67\left(x-9\right)$$

Use the distributive property to multiply 43 by x+15.

$$43x+645=67\left(x-9\right)$$

Use the distributive property to multiply 67 by x-9.

$$43x+645=67x-603$$

Subtract 67x from both sides.

$$43x+645-67x=-603$$

Combine 43x and -67x to get -24x.

$$-24x+645=-603$$

Subtract 645 from both sides.

$$-24x=-603-645$$

Subtract 645 from -603 to get -1248.

$$-24x=-1248$$

Divide both sides by -24.

$$x=\frac{-1248}{-24}$$

Divide -1248 by -24 to get 52.

$$x=52$$