Solve 4/2x+1+9/3x+2=25/5x+4

$$\frac { 4 } { 2 x + 1 } + \frac { 9 } { 3 x + 2 } = \frac { 25 } { 5 x + 4 }$$

Solve for x

$$x=-\frac{3}{5}=-0.6$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{4}{5},-\frac{2}{3},-\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by \left(2x+1\right)\left(3x+2\right)\left(5x+4\right), the least common multiple of 2x+1,3x+2,5x+4.

$$\left(3x+2\right)\left(5x+4\right)\times 4+\left(2x+1\right)\left(5x+4\right)\times 9=\left(2x+1\right)\left(3x+2\right)\times 25$$

Use the distributive property to multiply 3x+2 by 5x+4 and combine like terms.

$$\left(15x^{2}+22x+8\right)\times 4+\left(2x+1\right)\left(5x+4\right)\times 9=\left(2x+1\right)\left(3x+2\right)\times 25$$

Use the distributive property to multiply 15x^{2}+22x+8 by 4.

$$60x^{2}+88x+32+\left(2x+1\right)\left(5x+4\right)\times 9=\left(2x+1\right)\left(3x+2\right)\times 25$$

Use the distributive property to multiply 2x+1 by 5x+4 and combine like terms.

$$60x^{2}+88x+32+\left(10x^{2}+13x+4\right)\times 9=\left(2x+1\right)\left(3x+2\right)\times 25$$

Use the distributive property to multiply 10x^{2}+13x+4 by 9.

$$60x^{2}+88x+32+90x^{2}+117x+36=\left(2x+1\right)\left(3x+2\right)\times 25$$

Combine 60x^{2} and 90x^{2} to get 150x^{2}.

$$150x^{2}+88x+32+117x+36=\left(2x+1\right)\left(3x+2\right)\times 25$$

Combine 88x and 117x to get 205x.

$$150x^{2}+205x+32+36=\left(2x+1\right)\left(3x+2\right)\times 25$$

Add 32 and 36 to get 68.

$$150x^{2}+205x+68=\left(2x+1\right)\left(3x+2\right)\times 25$$

Use the distributive property to multiply 2x+1 by 3x+2 and combine like terms.

$$150x^{2}+205x+68=\left(6x^{2}+7x+2\right)\times 25$$

Use the distributive property to multiply 6x^{2}+7x+2 by 25.

$$150x^{2}+205x+68=150x^{2}+175x+50$$

Subtract 150x^{2} from both sides.

$$150x^{2}+205x+68-150x^{2}=175x+50$$

Combine 150x^{2} and -150x^{2} to get 0.

$$205x+68=175x+50$$

Subtract 175x from both sides.

$$205x+68-175x=50$$

Combine 205x and -175x to get 30x.

$$30x+68=50$$

Subtract 68 from both sides.

$$30x=50-68$$

Subtract 68 from 50 to get -18.

$$30x=-18$$

Divide both sides by 30.

$$x=\frac{-18}{30}$$

Reduce the fraction \frac{-18}{30} to lowest terms by extracting and canceling out 6.

$$x=-\frac{3}{5}$$