Question
I need some help with this question I really don't understand it and some help going through this problem would be really appreciated :)
Use the fact that a/b/c/d=a/b / c/d to simplify each rational expression. State any restrictions on the variables.
x^2-1/x^2-9 / x^2+3x-4/x^2+8x+15
Use the fact that a/b/c/d=a/b / c/d to simplify each rational expression. State any restrictions on the variables.
x^2-1/x^2-9 / x^2+3x-4/x^2+8x+15
Answers
actually, as written, the equation is not true, but we'll let that go.
When you divide by fractions, you invert and multiply:
(a/b) / (c/d) = (a/b)(d/c) = ad/bc
So, you have
(x^2-1/x^2-9)(x^2+8x+15/x^2+3x-4)
Now just factor everybody and start cancelling:
(x-1)(x+1)(x+3)(x+5)
-------------------------
(x-3)(x+3)(x+4)(x-1)
(x+1)(x+5)
---------------
(x-3)(x+4)
No values of x which make any of the denominators (in the original expression, or the result) zero are allowed.
When you divide by fractions, you invert and multiply:
(a/b) / (c/d) = (a/b)(d/c) = ad/bc
So, you have
(x^2-1/x^2-9)(x^2+8x+15/x^2+3x-4)
Now just factor everybody and start cancelling:
(x-1)(x+1)(x+3)(x+5)
-------------------------
(x-3)(x+3)(x+4)(x-1)
(x+1)(x+5)
---------------
(x-3)(x+4)
No values of x which make any of the denominators (in the original expression, or the result) zero are allowed.
bobpursley
on the abcd, b nor c, nor d can be zero
go one step further on the abcd
it also equals ad/bc
(x^2-1)((x^2+8x+15)/(x^2-9)(x^2+3x-4)
now to do some factoring..
(x+1)(x-1)(x+5)(x+3)/(x+3)(x-3)(x+4)(x-1)
do some dividing out..
(x+1)(x+5)/(x-3)(x+4)
note that x cannot be 3, nor -4
go one step further on the abcd
it also equals ad/bc
(x^2-1)((x^2+8x+15)/(x^2-9)(x^2+3x-4)
now to do some factoring..
(x+1)(x-1)(x+5)(x+3)/(x+3)(x-3)(x+4)(x-1)
do some dividing out..
(x+1)(x+5)/(x-3)(x+4)
note that x cannot be 3, nor -4
I am so very confused :(