How do you simplify $\frac{t^{2} - 25}{t^{2} + t - 20}$ $(t^2-25)/(t^2+t-20)$ ?

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How do you simplify $\frac{t^{2} - 25}{t^{2} + t - 20}$ $(t^2-25)/(t^2+t-20)$ ?

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Answer 1 · 2015-10-08T04:36:27

$\frac{t - 5}{t - 4}$ $(t - 5)/(t -4)$

Explanation:

Let's simplify both the numerator and denominator separately, we will start with the top:

$t^{2} - 25$ $t^2 - 25$

Using the difference of squares, I come up with the factored form

$(t - 5) (t + 5)$ $(t-5)(t+5)$

Let's save that for later, and jump to the bottom

$t^{2} + t - 20$ $t^2 + t - 20$

If I think to myself the factors of -20 that add to 1, I get the numbers 5 and -4. This brings me to the factored form:

$(t - 4) (t + 5)$ $(t - 4)(t + 5)$

Now putting the entire thing together, we have:

$((t-5)cancel((t+5)))/((t-4)cancel((t+5)))$

One commonality is formed between the top and the bottom, and that is $(t+5)$ which we can then cancel from the top and the bottom. This leaves us with our answer

$(t-5)/(t-4)$

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How do you simplify $\frac{t^{2} - 25}{t^{2} + t - 20}$ $(t^2-25)/(t^2+t-20)$ ?

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How do you simplify (t^2-25)/(t^2+t-20)t2−25t2+t−20(t^2-25)/(t^2+t-20)?

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How do you simplify $\frac{t^{2} - 25}{t^{2} + t - 20}$ $(t^2-25)/(t^2+t-20)$ ?