Solve 5/5x+2-2x+9/5x^2+17x+6=3/x+3

$$\frac { 5 } { 5 x + 2 } - \frac { 2 x + 9 } { 5 x ^ { 2 } + 17 x + 6 } = \frac { 3 } { x + 3 }$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -3,-\frac{2}{5} since division by zero is not defined. Multiply both sides of the equation by \left(x+3\right)\left(5x+2\right), the least common multiple of 5x+2,5x^{2}+17x+6,x+3.

$$\left(x+3\right)\times 5-\left(2x+9\right)=\left(5x+2\right)\times 3$$

Use the distributive property to multiply x+3 by 5.

$$5x+15-\left(2x+9\right)=\left(5x+2\right)\times 3$$

To find the opposite of 2x+9, find the opposite of each term.

$$5x+15-2x-9=\left(5x+2\right)\times 3$$

Combine 5x and -2x to get 3x.

$$3x+15-9=\left(5x+2\right)\times 3$$

Subtract 9 from 15 to get 6.

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

Use the distributive property to multiply 5x+2 by 3.

$$3x+6=15x+6$$

Subtract 15x from both sides.

$$3x+6-15x=6$$

Combine 3x and -15x to get -12x.

$$-12x+6=6$$

Subtract 6 from both sides.

$$-12x=6-6$$

Subtract 6 from 6 to get 0.

$$-12x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -12 is not equal to 0, x must be equal to 0.

$$x=0$$