What is ((4x^2-12x+9))/((4x^2-9)) ?

The solution to ((4x^2-12x+9))/((4x^2-9)) is (2x-3)/(2x+3)

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simplify ((4x^2-12x+9))/((4x^2-9))

simplify

\frac{( 4 x ^{2} - 12 x + 9 )}{( 4 x ^{2} - 9 )}

\frac{2 x - 3}{2 x + 3}

Solution steps

\frac{4 x ^{2} - 12 x + 9}{4 x ^{2} - 9}

Factor

4 x^{2} - 12 x + 9 : (2 x - 3)^{2}

= \frac{( 2 x - 3 ) ^{2}}{4 x ^{2} - 9}

Factor

4 x^{2} - 9 : (2 x + 3) (2 x - 3)

= \frac{( 2 x - 3 ) ^{2}}{( 2 x + 3 ) ( 2 x - 3 )}

Apply exponent rule:

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

(2 x - 3)^{2} = (2 x - 3) (2 x - 3)

= \frac{( 2 x - 3 ) ( 2 x - 3 )}{( 2 x + 3 ) ( 2 x - 3 )}

Cancel the common factor:

2 x - 3

= \frac{2 x - 3}{2 x + 3}

\frac{( 3 - 3 b ) ^{2} - 1}{4 \cdot b}

\frac{( x ^{2} + 2 x )}{( x ^{2} + 4 x + 4 )}

(d^{3} - 2 d)^{4}

(4 - d)^{3}

\frac{( - 3 x ^{5} y ^{3} )}{( - 4 x ^{2} y )}

What is ((4x^2-12x+9))/((4x^2-9)) ?
The solution to ((4x^2-12x+9))/((4x^2-9)) is (2x-3)/(2x+3)