Solve 4/x+3+1,5/x=1/2*31/x^2+3x

$$\frac { 4 } { x + 3 } + \frac { 1,5 } { x } = \frac { 1 } { 2 } \cdot \frac { 31 } { x ^ { 2 } + 3 x }$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -3;0 since division by zero is not defined. Multiply both sides of the equation by 2x\left(x+3\right), the least common multiple of x+3;x;2;x^{2}+3x.

$$2x\times 4+\left(2x+6\right)\times 1,5=\frac{1}{2}\times 2\times 31$$

Multiply 2 and 4 to get 8.

$$8x+\left(2x+6\right)\times 1,5=\frac{1}{2}\times 2\times 31$$

Use the distributive property to multiply 2x+6 by 1,5.

$$8x+3x+9=\frac{1}{2}\times 2\times 31$$

Combine 8x and 3x to get 11x.

$$11x+9=\frac{1}{2}\times 2\times 31$$

Multiply \frac{1}{2} and 2 to get 1.

$$11x+9=31$$

Subtract 9 from both sides.

$$11x=31-9$$

Subtract 9 from 31 to get 22.

$$11x=22$$

Divide both sides by 11.

$$x=\frac{22}{11}$$

Divide 22 by 11 to get 2.

$$x=2$$