Solve x+5/x+5x/x+5=6

$$\frac { x + 5 } { x } + \frac { 5 x } { x + 5 } = 6$$

Solve for x

$$x = \frac{5}{4} = 1\frac{1}{4} = 1.25$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -5,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+5\right), the least common multiple of x,x+5.

$$\left(x+5\right)\left(x+5\right)+x\times 5x=6x\left(x+5\right)$$

Multiply x+5 and x+5 to get \left(x+5\right)^{2}.

$$\left(x+5\right)^{2}+x\times 5x=6x\left(x+5\right)$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+5\right)^{2}.

$$x^{2}+10x+25+x\times 5x=6x\left(x+5\right)$$

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

$$x^{2}+10x+25+x^{2}\times 5=6x\left(x+5\right)$$

Combine x^{2} and x^{2}\times 5 to get 6x^{2}.

$$6x^{2}+10x+25=6x\left(x+5\right)$$

Use the distributive property to multiply 6x by x+5.

$$6x^{2}+10x+25=6x^{2}+30x$$

Subtract 6x^{2} from both sides.

$$6x^{2}+10x+25-6x^{2}=30x$$

Combine 6x^{2} and -6x^{2} to get 0.

$$10x+25=30x$$

Subtract 30x from both sides.

$$10x+25-30x=0$$

Combine 10x and -30x to get -20x.

$$-20x+25=0$$

Subtract 25 from both sides. Anything subtracted from zero gives its negation.

$$-20x=-25$$

Divide both sides by -20.

$$x=\frac{-25}{-20}$$

Reduce the fraction \frac{-25}{-20} to lowest terms by extracting and canceling out -5.

$$x=\frac{5}{4}$$