What is (25x-5)/(25x^2-10x+1) ?

The solution to (25x-5)/(25x^2-10x+1) is 5/(5x-1)

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simplify (25x-5)/(25x^2-10x+1)

simplify

\frac{25 x - 5}{25 x ^{2} - 10 x + 1}

\frac{5}{5 x - 1}

Solution steps

\frac{25 x - 5}{25 x ^{2} - 10 x + 1}

Factor

25 x - 5 : 5 (5 x - 1)

= \frac{5 ( 5 x - 1 )}{25 x ^{2} - 10 x + 1}

Factor

25 x^{2} - 10 x + 1 : (5 x - 1)^{2}

= \frac{5 ( 5 x - 1 )}{( 5 x - 1 ) ^{2}}

Apply exponent rule:

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

(5 x - 1)^{2} = (5 x - 1) (5 x - 1)

= \frac{5 ( 5 x - 1 )}{( 5 x - 1 ) ( 5 x - 1 )}

Cancel the common factor:

5 x - 1

= \frac{5}{5 x - 1}

x^{3} + 4 x^{2} - 3 x - 12

\frac{x ^{4}}{4} - x^{3} + x^{2}

5 - 75

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

\frac{x}{x ^{2} - 16} - \frac{4}{x ^{2} + 5 x + 4}

What is (25x-5)/(25x^2-10x+1) ?
The solution to (25x-5)/(25x^2-10x+1) is 5/(5x-1)