Solve 4x+1/4x-1-6/16x^2-1=4x-1/4x+1

$$\frac { 4 x + 1 } { 4 x - 1 } - \frac { 6 } { 16 x ^ { 2 } - 1 } = \frac { 4 x - 1 } { 4 x + 1 }$$

Solve for x

$$x=\frac{3}{8}=0.375$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{1}{4},\frac{1}{4} since division by zero is not defined. Multiply both sides of the equation by \left(4x-1\right)\left(4x+1\right), the least common multiple of 4x-1,16x^{2}-1,4x+1.

$$\left(4x+1\right)\left(4x+1\right)-6=\left(4x-1\right)\left(4x-1\right)$$

Multiply 4x+1 and 4x+1 to get \left(4x+1\right)^{2}.

$$\left(4x+1\right)^{2}-6=\left(4x-1\right)\left(4x-1\right)$$

Multiply 4x-1 and 4x-1 to get \left(4x-1\right)^{2}.

$$\left(4x+1\right)^{2}-6=\left(4x-1\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(4x+1\right)^{2}.

$$16x^{2}+8x+1-6=\left(4x-1\right)^{2}$$

Subtract 6 from 1 to get -5.

$$16x^{2}+8x-5=\left(4x-1\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4x-1\right)^{2}.

$$16x^{2}+8x-5=16x^{2}-8x+1$$

Subtract 16x^{2} from both sides.

$$16x^{2}+8x-5-16x^{2}=-8x+1$$

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

$$8x-5=-8x+1$$

Add 8x to both sides.

$$8x-5+8x=1$$

Combine 8x and 8x to get 16x.

$$16x-5=1$$

Add 5 to both sides.

$$16x=1+5$$

Add 1 and 5 to get 6.

$$16x=6$$

Divide both sides by 16.

$$x=\frac{6}{16}$$

Reduce the fraction \frac{6}{16} to lowest terms by extracting and canceling out 2.

$$x=\frac{3}{8}$$