Question

Help please :)
-3<(x2+ax-2)/(x2-x+1)<2

Answer 1

are you trying to solve for a or x?

Answer 2

oops sorry. given that this equality is true for all values of x, find the range of values for a

Answer 3

so one way to solve it would be to split it into two inqualities and multiply both sides by the denominator so -3x^2+3x-3<x^2+ax-2 and x^2+ax-2<2x^2-2x+2 and then solve those two inequalities

Answer 4

no? i thought you can't just multiply by the denominator because there is a possibiltiy the denominator is negative, hence the inequality sign might flip

Answer 5

oh, yea, sorry i'm afraid i can't help you then :(

Answer 6

haha it's ok thankyou ：）

Answer 7

hold on a sec.

Answer 8

Well, for -3x^2+3x-3<x^2+ax-2, the answer is a>−4x2+3x−1/x
x

Answer 9

But if you want to answer this question yourself, go to mathpapa a really advanced calculator.

Answer 10

@wcrmelissa2001 this one you can multiply both sides by the denominator.

The reason is that x^2 - x + 1 = (x-0.5)^2 + 3/4 > 0 (complete the square) so the denominator is definitely positive for all values of x

Answer 11

haha i just got that too before seeing this @mww :D
THANKS EVERYONE!