Solve 3x+1/x=9x+4/3x+1

$$\frac{ 3x+1 }{ x } = \frac{ 9x+4 }{ 3x+1 }$$

Solve for x

$$x=-\frac{1}{2}=-0.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{1}{3},0 since division by zero is not defined. Multiply both sides of the equation by x\left(3x+1\right), the least common multiple of x,3x+1.

$$\left(3x+1\right)\left(3x+1\right)=x\left(9x+4\right)$$

Multiply 3x+1 and 3x+1 to get \left(3x+1\right)^{2}.

$$\left(3x+1\right)^{2}=x\left(9x+4\right)$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+1\right)^{2}.

$$9x^{2}+6x+1=x\left(9x+4\right)$$

Use the distributive property to multiply x by 9x+4.

$$9x^{2}+6x+1=9x^{2}+4x$$

Subtract 9x^{2} from both sides.

$$9x^{2}+6x+1-9x^{2}=4x$$

Combine 9x^{2} and -9x^{2} to get 0.

$$6x+1=4x$$

Subtract 4x from both sides.

$$6x+1-4x=0$$

Combine 6x and -4x to get 2x.

$$2x+1=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$2x=-1$$

Divide both sides by 2.

$$x=\frac{-1}{2}$$

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$x=-\frac{1}{2}$$