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

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

Solve for x

$$x=-\frac{47}{52}\approx -0.903846154$$

Steps for Solving Linear Equation

Variable x cannot be equal to -\frac{5}{4} since division by zero is not defined. Multiply both sides of the equation by 4x+5.

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

Use the distributive property to multiply 2 by 4x+5.

$$\left(8x+10\right)\left(1-4x\right)^{-1}\left(1+x\right)\times 2^{2}+\left(4x+5\right)\times 2=3$$

Use the distributive property to multiply 8x+10 by \left(1-4x\right)^{-1}.

$$\left(8x\left(1-4x\right)^{-1}+10\left(1-4x\right)^{-1}\right)\left(1+x\right)\times 2^{2}+\left(4x+5\right)\times 2=3$$

Use the distributive property to multiply 8x\left(1-4x\right)^{-1}+10\left(1-4x\right)^{-1} by 1+x and combine like terms.

$$\left(18x\left(1-4x\right)^{-1}+8\left(1-4x\right)^{-1}x^{2}+10\left(1-4x\right)^{-1}\right)\times 2^{2}+\left(4x+5\right)\times 2=3$$

Calculate 2 to the power of 2 and get 4.

$$\left(18x\left(1-4x\right)^{-1}+8\left(1-4x\right)^{-1}x^{2}+10\left(1-4x\right)^{-1}\right)\times 4+\left(4x+5\right)\times 2=3$$

Use the distributive property to multiply 18x\left(1-4x\right)^{-1}+8\left(1-4x\right)^{-1}x^{2}+10\left(1-4x\right)^{-1} by 4.

$$72\left(1-4x\right)^{-1}x+32\left(1-4x\right)^{-1}x^{2}+40\left(1-4x\right)^{-1}+\left(4x+5\right)\times 2=3$$

Use the distributive property to multiply 4x+5 by 2.

$$72\left(1-4x\right)^{-1}x+32\left(1-4x\right)^{-1}x^{2}+40\left(1-4x\right)^{-1}+8x+10=3$$

Subtract 10 from both sides.

$$72\left(1-4x\right)^{-1}x+32\left(1-4x\right)^{-1}x^{2}+40\left(1-4x\right)^{-1}+8x=3-10$$

Subtract 10 from 3 to get -7.

$$72\left(1-4x\right)^{-1}x+32\left(1-4x\right)^{-1}x^{2}+40\left(1-4x\right)^{-1}+8x=-7$$

Reorder the terms.

$$32\times \frac{1}{-4x+1}x^{2}+8x+72\times \frac{1}{-4x+1}x+40\times \frac{1}{-4x+1}=-7$$

Variable x cannot be equal to \frac{1}{4} since division by zero is not defined. Multiply both sides of the equation by -4x+1.

$$32\times 1x^{2}+8x\left(-4x+1\right)+72\times 1x+40\times 1=-7\left(-4x+1\right)$$

Do the multiplications.

$$32x^{2}+8x\left(-4x+1\right)+72x+40=-7\left(-4x+1\right)$$

Use the distributive property to multiply 8x by -4x+1.

$$32x^{2}-32x^{2}+8x+72x+40=-7\left(-4x+1\right)$$

Combine 32x^{2} and -32x^{2} to get 0.

$$8x+72x+40=-7\left(-4x+1\right)$$

Combine 8x and 72x to get 80x.

$$80x+40=-7\left(-4x+1\right)$$

Use the distributive property to multiply -7 by -4x+1.

$$80x+40=28x-7$$

Subtract 28x from both sides.

$$80x+40-28x=-7$$

Combine 80x and -28x to get 52x.

$$52x+40=-7$$

Subtract 40 from both sides.

$$52x=-7-40$$

Subtract 40 from -7 to get -47.

$$52x=-47$$

Divide both sides by 52.

$$x=\frac{-47}{52}$$

Fraction \frac{-47}{52} can be rewritten as -\frac{47}{52} by extracting the negative sign.

$$x=-\frac{47}{52}$$