Mathematics
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OpenStudy (anonymous):
Which sum is equal to
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OpenStudy (anonymous):
OpenStudy (anonymous):
factorise the numeretor
Parth (parthkohli):
Factor the numerator and denominator. Cancel to conclude your answer.
Parth (parthkohli):
\( \color{Black}{\Rightarrow x^2 - 25 = \cdots }\)
This follows the difference of squares formula.
OpenStudy (anonymous):
\[a^2 - b^2 = (a+b)(a-b)\]
Here a = x and b = 5
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Parth (parthkohli):
\( \color{Black}{\Rightarrow (x)^2 - (5)^2 = ?}\)
OpenStudy (anonymous):
(x-5)(x+5)
OpenStudy (anonymous):
Yes..
OpenStudy (anonymous):
okay so now I do that to the top
OpenStudy (anonymous):
Now factorize the numerator..
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OpenStudy (anonymous):
(x+5)(x-1)
OpenStudy (anonymous):
or the other way
OpenStudy (anonymous):
Yes you are absolutely right..
OpenStudy (anonymous):
Now see what you cancel in top and bottom??
OpenStudy (anonymous):
so the answer would be
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OpenStudy (anonymous):
No...
OpenStudy (anonymous):
See now show me after factorization what you get..
Write both numerator and denominator..
OpenStudy (anonymous):
x-5/x-5 + x+1/x+5
OpenStudy (anonymous):
\[\frac{(x+5)(x-1)}{(x+5)(x-5)}\]
Parth (parthkohli):
Something now cancels.
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OpenStudy (anonymous):
How does + comes in between??
You have factored the things so multiply will come between them..
OpenStudy (anonymous):
I forgot to do the step in between
OpenStudy (anonymous):
Now tell me what is getting cancelled there in the numerator and denominator??
OpenStudy (anonymous):
(x+5)
OpenStudy (anonymous):
Yes then cancel it and what are you left with??
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OpenStudy (anonymous):
(x-1)/(x-5)
OpenStudy (anonymous):
And this is your answer..
OpenStudy (anonymous):
Or you can write it as:
\[\frac{x}{x-5} - \frac{1}{x-5}\]
OpenStudy (anonymous):
okay thank you
OpenStudy (anonymous):
Welcome dear..