What is (x^2-14x+49)/(6x^2-42x) ?

The solution to (x^2-14x+49)/(6x^2-42x) is (x-7)/(6x)

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simplify (x^2-14x+49)/(6x^2-42x)

simplify

\frac{x ^{2} - 14 x + 49}{6 x ^{2} - 42 x}

\frac{x - 7}{6 x}

Solution steps

\frac{x ^{2} - 14 x + 49}{6 x ^{2} - 42 x}

Factor

x^{2} - 14 x + 49 : (x - 7)^{2}

= \frac{( x - 7 ) ^{2}}{6 x ^{2} - 42 x}

Factor

6 x^{2} - 42 x : 6 x (x - 7)

= \frac{( x - 7 ) ^{2}}{6 x ( x - 7 )}

Apply exponent rule:

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

(x - 7)^{2} = (x - 7) (x - 7)

= \frac{( x - 7 ) ( x - 7 )}{6 x ( x - 7 )}

Cancel the common factor:

x - 7

= \frac{x - 7}{6 x}

\frac{2 x ^{2} + 4 x}{x ^{2} + 5 x + 6}

(2 a - 3) (a + 3)

10 x - 8 x + 2 + 10

(- 5 i) (- 3 i)

\frac{15}{27}

What is (x^2-14x+49)/(6x^2-42x) ?
The solution to (x^2-14x+49)/(6x^2-42x) is (x-7)/(6x)