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

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

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

simplify

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

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

Solution steps

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

Factor

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

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

Factor

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

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

Cancel the common factor:

5 x - 1

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

(i) 3 x^{2} + 6 x - 24

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

2 x^{4} y - 35 x^{3} y

3 x^{2} y + 2 x^{2}

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