Solve x/5+3=2/x+x+1/5

$$\frac { x } { 5 } + 3 = \frac { 2 } { x } + \frac { x + 1 } { 5 }$$

Solve for x

$$x=\frac{5}{7}\approx 0.714285714$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 5x, the least common multiple of 5,x.

$$xx+5x\times 3=5\times 2+x\left(x+1\right)$$

Multiply x and x to get x^{2}.

$$x^{2}+5x\times 3=5\times 2+x\left(x+1\right)$$

Multiply 5 and 3 to get 15.

$$x^{2}+15x=5\times 2+x\left(x+1\right)$$

Multiply 5 and 2 to get 10.

$$x^{2}+15x=10+x\left(x+1\right)$$

Use the distributive property to multiply x by x+1.

$$x^{2}+15x=10+x^{2}+x$$

Subtract x^{2} from both sides.

$$x^{2}+15x-x^{2}=10+x$$

Combine x^{2} and -x^{2} to get 0.

$$15x=10+x$$

Subtract x from both sides.

$$15x-x=10$$

Combine 15x and -x to get 14x.

$$14x=10$$

Divide both sides by 14.

$$x=\frac{10}{14}$$

Reduce the fraction \frac{10}{14} to lowest terms by extracting and canceling out 2.

$$x=\frac{5}{7}$$