Question

Please help me with this question:

(x^2+5x+4)/(x+4) - (x^2-5x+6)/(x-2)

the answer is 4 but I dont know how

Answer 1

the first quadratic has a factorization that includes (x+4), that leaves the other factor, similar with the other term, your answer should be 4.

Answer 2

can you show me a step by step method?

Answer 3

Factor x^2 + 5x +4
What two numbers multiply to give you 4 and add to give you 5?

Answer 4

ab=4 and a+b=5, can you guess?

Answer 5

The possibilities for ab=4 are 1*4, 2*2 and lots of other non integers, but let's just stick with integers

Answer 6

Which of the two pairs would work to give a+b=5?

Answer 7

41

Answer 8

4 and 1

Answer 9

ok, those are your factors for the 1st term, because (x^2+5x+4) = (x+4)(x+1) = x^2 + 4x + 1x + (4*1) = x^2 + x(4+1) + 4*1 = x^2 + 4(a +b) + a*b, this is where the a and b come into the picture.

Answer 10

Do you see here why we needed ab=4 and a+b=5?

Answer 11

yeah

Answer 12

For x^2-5x+6, what a and b factors multiply to give 6 but add to give -5?

Answer 13

but how does the entire thing equal 4 especially when we need the common denominators?



1 and 6

-6 +1

Answer 14

so the factors are (x-6)(x+1), multiply out to ensure they produce the correct result

Answer 15

Factors should have been -2 and -3, actually

Answer 16

Now you have your factors. Replace the quadratics in the numerator with these factors.

Answer 17

(You will see 4 pop out when you simplify everything)

Answer 18

Thank you so much. Can you help me with the other question too? i did the same things u told me but didnt get the answer

Answer 19

sure