What is (4x^2-1)/(4x^2+4x+1) ?

The solution to (4x^2-1)/(4x^2+4x+1) is (2x-1)/(2x+1)

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simplify (4x^2-1)/(4x^2+4x+1)

simplify

\frac{4 x ^{2} - 1}{4 x ^{2} + 4 x + 1}

\frac{2 x - 1}{2 x + 1}

Solution steps

\frac{4 x ^{2} - 1}{4 x ^{2} + 4 x + 1}

Factor

4 x^{2} - 1 : (2 x + 1) (2 x - 1)

= \frac{( 2 x + 1 ) ( 2 x - 1 )}{4 x ^{2} + 4 x + 1}

Factor

4 x^{2} + 4 x + 1 : (2 x + 1)^{2}

= \frac{( 2 x + 1 ) ( 2 x - 1 )}{( 2 x + 1 ) ^{2}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(2 x + 1)^{2} = (2 x + 1) (2 x + 1)

= \frac{( 2 x + 1 ) ( 2 x - 1 )}{( 2 x + 1 ) ( 2 x + 1 )}

Cancel the common factor:

2 x + 1

= \frac{2 x - 1}{2 x + 1}

x (x + 1)^{3}

4 - y^{2}

- 6 x^{4} - 27 x^{3}

\frac{1}{2} \cdot (- 6)

What is (4x^2-1)/(4x^2+4x+1) ?
The solution to (4x^2-1)/(4x^2+4x+1) is (2x-1)/(2x+1)