How come a – b/(a – b)(a + b), can be simplified to 1/a + b?

Answer 1

Best Answer - Chosen by Asker

you factor our the (a - b)......
like this

same as

(2 * 3) / (2 * 4) = 3 / 4 ....factor out the 2s

verify....

6 / 8 = 3/4, correct

so back to your equation......

(a - b) / (a - b)(a + b) the (a- b) / (a - b) factors out to...1 / 1

1 / 1(a + b) = 1 / (a + b)

verify....by adding in some constants.....(a = 9 b = 5)

(9 - 5) / (9 - 5)(9 + 5)
4 / 4 * 14
4 / 56
1 / 14

simplified way.....

(9 - 5) / (9 - 5)(9 + 5)
1 / (9 + 5)
1 / 14

Asker's Rating:

Asker's Comment:

great, straightforward and with further examples. THANKS!

Answer 2

Simple:

Step1: Let C represent a-b and let D represent a+b


Step2: a-b/(a-b)(a+b) will read C/CxD

Step3: divide your numerator by C = C/C =1

Step4: divide your denominator by C = C x D/C = D

Step5: divide the answer in Step3 by the answer in Step4
and you now have 1/D

Step 6: expand D to its original form: D = a+b
C now is equal to 1

Therefore C/D = 1/a+b

finally therefore a - b/(a-b)(a+b) = 1/a+b.

Answer 3

it cancel out the top (a-b) with the bottom (a-b) and we write 1 because with only one function like this one top and only one on the bottom. So, the answer it will be 1/(a+b) or (a+b)^-1

Answer 4

A number divided by itself is 1.

(a-b) / (a-b) = 1, leaving a 1 on both sides of the division, turning it into 1/(a+b)

Answer 5

The (a - b) in the numerator and (a - b) in the denominator cancel out to 1.

You are left with 1 / (a + b).

Source(s):

Self

Answer 6

simple just cancel out (a-b)

then only 1/(a+b) will remain.......

Answer 7

(a – b) / (a – b)(a + b) = 1 / (a + b)