What is (4x^2-12x+9)/(8x^2-18) ?

The solution to (4x^2-12x+9)/(8x^2-18) is (2x-3)/(2(2x+3))

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simplify (4x^2-12x+9)/(8x^2-18)

simplify

\frac{4 x ^{2} - 12 x + 9}{8 x ^{2} - 18}

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

Solution steps

\frac{4 x ^{2} - 12 x + 9}{8 x ^{2} - 18}

Factor

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

= \frac{( 2 x - 3 ) ^{2}}{8 x ^{2} - 18}

Factor

8 x^{2} - 18 : 2 (2 x + 3) (2 x - 3)

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

Cancel the common factor:

2 x - 3

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

(3 x^{2} + x - 4) (2 x - 5)

\frac{7 x - 14}{x - 2}

\frac{4}{9 x ^{2} - 45 x} - \frac{6 x}{x ^{2} - 25}

3 6^{0.5}

a (a - x) + 3 a (x + 2 a) - a (x - 3 a)

What is (4x^2-12x+9)/(8x^2-18) ?
The solution to (4x^2-12x+9)/(8x^2-18) is (2x-3)/(2(2x+3))