Solve 4/x=1/x^2+4x-x+3/x^2+4x

$$\frac { 4 } { x } = \frac { 1 } { x ^ { 2 } + 4 x } - \frac { x + 3 } { x ^ { 2 } + 4 x }$$

Solve for x

$$x = -\frac{18}{5} = -3\frac{3}{5} = -3.6$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -4,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+4\right), the least common multiple of x,x^{2}+4x.

$$\left(x+4\right)\times 4=1-\left(x+3\right)$$

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

$$4x+16=1-\left(x+3\right)$$

To find the opposite of x+3, find the opposite of each term.

$$4x+16=1-x-3$$

Subtract 3 from 1 to get -2.

$$4x+16=-2-x$$

Add x to both sides.

$$4x+16+x=-2$$

Combine 4x and x to get 5x.

$$5x+16=-2$$

Subtract 16 from both sides.

$$5x=-2-16$$

Subtract 16 from -2 to get -18.

$$5x=-18$$

Divide both sides by 5.

$$x=\frac{-18}{5}$$

Fraction \frac{-18}{5} can be rewritten as -\frac{18}{5} by extracting the negative sign.

$$x=-\frac{18}{5}$$