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Here, we show you a step-by-step solved example of limits. This solution was automatically generated by our smart calculator:
lim β‘ x β β
5 ( x 2 β 25 x β 5 ) \lim_{x\to\:5}\left(\frac{x^2-25}{x-5}\right) x β 5 lim β ( x β 5 x 2 β 25 β )
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Intermediate steps
Simplify x 2 \sqrt{x^2} x 2 β ( a m ) n = a m β
n \left(a^m\right)^n=a^{m\cdot n} ( a m ) n = a m β
n m m m 2 2 2 n n n 1 2 \frac{1}{2} 2 1 β
( x + 25 ) ( x 2 β 25 ) x β 5 \frac{\left(x+\sqrt{25}\right)\left(\sqrt{x^2}-\sqrt{25}\right)}{x-5} x β 5 ( x + 25 β ) ( x 2 β β 25 β ) β
Calculate the power 25 \sqrt{25} 25 β
( x + 5 ) ( x 2 β 25 ) x β 5 \frac{\left(x+5\right)\left(\sqrt{x^2}-\sqrt{25}\right)}{x-5} x β 5 ( x + 5 ) ( x 2 β β 25 β ) β
Simplify x 2 \sqrt{x^2} x 2 β ( a m ) n = a m β
n \left(a^m\right)^n=a^{m\cdot n} ( a m ) n = a m β
n m m m 2 2 2 n n n 1 2 \frac{1}{2} 2 1 β
( x + 5 ) ( x β 25 ) x β 5 \frac{\left(x+5\right)\left(x-\sqrt{25}\right)}{x-5} x β 5 ( x + 5 ) ( x β 25 β ) β
Calculate the power 25 \sqrt{25} 25 β
( x + 5 ) ( x β 5 ) x β 5 \frac{\left(x+5\right)\left(x- 5\right)}{x-5} x β 5 ( x + 5 ) ( x β 5 ) β
Multiply β 1 -1 β 1 5 5 5
( x + 5 ) ( x β 5 ) x β 5 \frac{\left(x+5\right)\left(x-5\right)}{x-5} x β 5 ( x + 5 ) ( x β 5 ) β
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Factor the difference of squares x 2 β 25 x^2-25 x 2 β 25
( x + 5 ) ( x β 5 ) x β 5 \frac{\left(x+5\right)\left(x-5\right)}{x-5} x β 5 ( x + 5 ) ( x β 5 ) β
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Explain this step further
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Simplify the fraction ( x + 5 ) ( x β 5 ) x β 5 \frac{\left(x+5\right)\left(x-5\right)}{x-5} x β 5 ( x + 5 ) ( x β 5 ) β x β 5 x-5 x β 5
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Evaluate the limit lim β‘ x β 5 ( x + 5 ) \lim_{x\to5}\left(x+5\right) lim x β 5 β ( x + 5 ) x x x 5 5 5
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Add the values 5 5 5 5 5 5
ξ Final answer to the exercise