7/(x-2)(x+5)-8/(x+5)(x-3)

Question

7(x-3)-8(x-2)/(x-2)(x+5)(x-3)

7x-21-8x+16/(x-2)(x+5)(x-3)

7x-8x give me -1x and -21+16 give me -5. for numerator but it have to be -1/(x-2)(x-3)

i not know how to do this please explain process my way not different way.

Answer 1

You have to use brackets to show that both
x-2 and x+5 are factors of the bottom, so ...
7/((x-2)(x+5)) - 8/((x+5)(x-3)

so the lowest common denominator is (x-2)(x+5)(x-3)
we get
[ 7(x-3) - 8(x-2) ] /[(x-2)(x+5)(x-3)]
= [7x - 21 - 8x + 16]/[(x-2)(x+5)(x-3)]
= (-x - 5)/[(x-2)(x+5)(x-3)]
= -1(x+5)/[(x-2)(x+5)(x-3)]
= -1/[(x-2)(x-3)]

Answer 2

= (-x - 5)/[(x-2)(x+5)(x-3)]
i understand how u do this part

= -1(x+5)/[(x-2)(x+5)(x-3)]
i not understand how you get numerator

Answer 3

I simply factored out a -1

Answer 4

sorry but that the only thing i don't understand how do u factor that out? could you please explains slowly

Answer 5

suppose you had

2x + 4
then it would be 2(x+2)

suppose you had
-2x - 4
then it would be -2(x+2)

suppose you had -x -5
then it would be -1(x+5)

in each case, expand my answer and see what you get.

Answer 6

thank you very much reiny for taking time to explain :) u took all confusion away :)