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Simplify this problem

Simplify this problem-example-1

2 Answers

5 votes

(49 - (1)/(r^2) )/(7 - (1)/(r) )

Rewrite the fraction as division:

= (49 - (1)/(r^2)) / (7 - (1)/(r) )

Make them into single fraction:

= (49r^2 - 1)/(r^2) / (7r - 1)/(r)

Change the divide fraction into multiplication fraction:

= (49r^2 - 1)/(r^2) * (r)/(7r - 1)

Factorise the difference of square a² - b² = (a + b) (a - b) :

= ((7r+ 1)(7r - 1))/(r^2) * (r)/(7r - 1)

Cancel the common factors:

= ((7r+ 1))/(r)
User Yonatan Maman
by
8.0k points
4 votes
Comment. The best way to do this is to let 1/r = a and 1/r^2 = a^2. Now rewrite the problem.

Solution

(49 - a^2)/(7 - a) \\ ((7 - a)(7 + a))/(7 - a)\text{ Notice a cancellation can take place}

There is a 7 - a in both numerator and denominator, so that cancel providing a does not equal 7. a cannot equal 7 because that will put a 7 in the denominator and that makes the whole fraction = something over 0 which is undefined.

Answer
So far what we have is
7 + a

But a = 1/r
So the answer can be 7 + 1/r

r can be anything but 0 [for this answer]
and 1/7 for the cancellation.
User Noufal Kmc
by
8.7k points

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