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

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

Solve for x

$$x=-\frac{7}{12}\approx -0.583333333$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{3}{5},-\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by \left(2x+1\right)\left(5x+3\right), the least common multiple of 2x+1,5x+3.

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

Use the distributive property to multiply 5x+3 by 2x+3 and combine like terms.

$$10x^{2}+21x+9=\left(2x+1\right)\left(5x+2\right)$$

Use the distributive property to multiply 2x+1 by 5x+2 and combine like terms.

$$10x^{2}+21x+9=10x^{2}+9x+2$$

Subtract 10x^{2} from both sides.

$$10x^{2}+21x+9-10x^{2}=9x+2$$

Combine 10x^{2} and -10x^{2} to get 0.

$$21x+9=9x+2$$

Subtract 9x from both sides.

$$21x+9-9x=2$$

Combine 21x and -9x to get 12x.

$$12x+9=2$$

Subtract 9 from both sides.

$$12x=2-9$$

Subtract 9 from 2 to get -7.

$$12x=-7$$

Divide both sides by 12.

$$x=\frac{-7}{12}$$

Fraction \frac{-7}{12} can be rewritten as -\frac{7}{12} by extracting the negative sign.

$$x=-\frac{7}{12}$$