Solve x+6/4x^2+3/2x^2=x+4/2x^2

$$\frac { x + 6 } { 4 x ^ { 2 } } + \frac { 3 } { 2 x ^ { 2 } } = \frac { x + 4 } { 2 x ^ { 2 } }$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4x^{2}, the least common multiple of 4x^{2},2x^{2}.

$$x+6+2\times 3=2\left(x+4\right)$$

Multiply 2 and 3 to get 6.

$$x+6+6=2\left(x+4\right)$$

Add 6 and 6 to get 12.

$$x+12=2\left(x+4\right)$$

Use the distributive property to multiply 2 by x+4.

$$x+12=2x+8$$

Subtract 2x from both sides.

$$x+12-2x=8$$

Combine x and -2x to get -x.

$$-x+12=8$$

Subtract 12 from both sides.

$$-x=8-12$$

Subtract 12 from 8 to get -4.

$$-x=-4$$

Multiply both sides by -1.

$$x=4$$