Solve frac{x+sqrt{13}}{3sqrt{13}}=8/13

$$\frac { x + \sqrt { 13 } } { 3 \sqrt { 13 } } = \frac { 8 } { 13 }$$

Solve for x

$$x = \frac{11 \sqrt{13}}{13} \approx 3.050851079$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{x+\sqrt{13}}{3\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$\frac{\left(x+\sqrt{13}\right)\sqrt{13}}{3\left(\sqrt{13}\right)^{2}}=\frac{8}{13}$$

The square of \sqrt{13} is 13.

$$\frac{\left(x+\sqrt{13}\right)\sqrt{13}}{3\times 13}=\frac{8}{13}$$

Multiply 3 and 13 to get 39.

$$\frac{\left(x+\sqrt{13}\right)\sqrt{13}}{39}=\frac{8}{13}$$

Use the distributive property to multiply x+\sqrt{13} by \sqrt{13}.

$$\frac{x\sqrt{13}+\left(\sqrt{13}\right)^{2}}{39}=\frac{8}{13}$$

The square of \sqrt{13} is 13.

$$\frac{x\sqrt{13}+13}{39}=\frac{8}{13}$$

Multiply both sides by 39.

$$x\sqrt{13}+13=\frac{8}{13}\times 39$$

Express \frac{8}{13}\times 39 as a single fraction.

$$x\sqrt{13}+13=\frac{8\times 39}{13}$$

Multiply 8 and 39 to get 312.

$$x\sqrt{13}+13=\frac{312}{13}$$

Divide 312 by 13 to get 24.

$$x\sqrt{13}+13=24$$

Subtract 13 from both sides.

$$x\sqrt{13}=24-13$$

Subtract 13 from 24 to get 11.

$$x\sqrt{13}=11$$

The equation is in standard form.

$$\sqrt{13}x=11$$

Divide both sides by \sqrt{13}.

$$\frac{\sqrt{13}x}{\sqrt{13}}=\frac{11}{\sqrt{13}}$$

Dividing by \sqrt{13} undoes the multiplication by \sqrt{13}.

$$x=\frac{11}{\sqrt{13}}$$

Divide 11 by \sqrt{13}.

$$x=\frac{11\sqrt{13}}{13}$$