7/(x-2)(x+5)-8/(x+5)(x-3)
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.
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)]
= (-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
I simply factored out a -1
sorry but that the only thing i don't understand how do u factor that out? could you please explains slowly
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.
thank you very much reiny for taking time to explain :) u took all confusion away :)
Sure, I can explain the process in your way. Let's go step by step.
We start with the expression:
7/(x-2)(x+5) - 8/(x+5)(x-3)
To simplify this expression, we need to combine the fractions into a single fraction. To do that, we need a common denominator. Let's find the common denominator:
The factors in the denominator of the first fraction are (x-2) and (x+5).
The factors in the denominator of the second fraction are (x+5) and (x-3).
To find the common denominator, we need to consider all the factors. We have:
(x-2), (x+5), and (x-3).
Now, to combine these factors, we multiply them together:
Common denominator = (x-2)(x+5)(x-3)
Now, let's rewrite the expression using the common denominator:
7/(x-2)(x+5) - 8/(x+5)(x-3) = (7(x-3) - 8(x-2))/(x-2)(x+5)(x-3)
Next, we simplify the numerator using the distributive property:
7(x-3) - 8(x-2) = (7x - 21) - (8x - 16) = 7x - 21 - 8x + 16 = -1x - 5.
Finally, we substitute the simplified numerator back into the expression:
(-1x - 5)/(x-2)(x+5)(x-3)
So, the simplified expression is -1/(x-2)(x+5)(x-3).
That's it! We have simplified the expression step by step.