Solve 6x+1/3x-2=2x+5/x+3

$$\frac { 6 x + 1 } { 3 x - 2 } = \frac { 2 x + 5 } { x + 3 }$$

Solve for x

$$x = -\frac{13}{8} = -1\frac{5}{8} = -1.625$$

Steps for Solving Linear Equation

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

$$\left(x+3\right)\left(6x+1\right)=\left(3x-2\right)\left(2x+5\right)$$

Use the distributive property to multiply x+3 by 6x+1 and combine like terms.

$$6x^{2}+19x+3=\left(3x-2\right)\left(2x+5\right)$$

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

$$6x^{2}+19x+3=6x^{2}+11x-10$$

Subtract 6x^{2} from both sides.

$$6x^{2}+19x+3-6x^{2}=11x-10$$

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

$$19x+3=11x-10$$

Subtract 11x from both sides.

$$19x+3-11x=-10$$

Combine 19x and -11x to get 8x.

$$8x+3=-10$$

Subtract 3 from both sides.

$$8x=-10-3$$

Subtract 3 from -10 to get -13.

$$8x=-13$$

Divide both sides by 8.

$$x=\frac{-13}{8}$$

Fraction \frac{-13}{8} can be rewritten as -\frac{13}{8} by extracting the negative sign.

$$x=-\frac{13}{8}$$