Solve 1-4x/2x+2+2=3/4x+5

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

Solve for x

$$x = -\frac{19}{14} = -1\frac{5}{14} \approx -1.357142857$$

Steps for Solving Linear Equation

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

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

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

$$-16x-16x^{2}+5+2\left(x+1\right)\left(4x+5\right)\times 2=\left(2x+2\right)\times 3$$

Multiply 2 and 2 to get 4.

$$-16x-16x^{2}+5+4\left(x+1\right)\left(4x+5\right)=\left(2x+2\right)\times 3$$

Use the distributive property to multiply 4 by x+1.

$$-16x-16x^{2}+5+\left(4x+4\right)\left(4x+5\right)=\left(2x+2\right)\times 3$$

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

$$-16x-16x^{2}+5+16x^{2}+36x+20=\left(2x+2\right)\times 3$$

Combine -16x^{2} and 16x^{2} to get 0.

$$-16x+5+36x+20=\left(2x+2\right)\times 3$$

Combine -16x and 36x to get 20x.

$$20x+5+20=\left(2x+2\right)\times 3$$

Add 5 and 20 to get 25.

$$20x+25=\left(2x+2\right)\times 3$$

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

$$20x+25=6x+6$$

Subtract 6x from both sides.

$$20x+25-6x=6$$

Combine 20x and -6x to get 14x.

$$14x+25=6$$

Subtract 25 from both sides.

$$14x=6-25$$

Subtract 25 from 6 to get -19.

$$14x=-19$$

Divide both sides by 14.

$$x=\frac{-19}{14}$$

Fraction \frac{-19}{14} can be rewritten as -\frac{19}{14} by extracting the negative sign.

$$x=-\frac{19}{14}$$