Question

Simplify. Identify any x-values for which the expression is undefined.
\[\frac{ 6x ^{2}+7x-3 }{ -3x ^{2}+x }\]

Answer 1

Please help

Answer 2

ok first x values for which the expression is undefined
in order to find them we have to find the x values who makes the denominator 0

-3x^2 +x = 0
can you find them ?

Answer 3

Im not very good at this and am stuck thats the only reason im on here cause i have no clue and school in two hours

Answer 4

ok
so in order to solve -3x^2 + x =0
we take out one x since in 2 of the terms there is x

and get :

x (-3x + 1) = 0

now two solutions for this
x=0 or
-3x +1 = 0
and it means x = 1/3

so for x = 0 and x = 1/3 the expression is undifined

Answer 5

now the numerator can be simplify into
6x^2 +7x - 3
6x^2 +9x-2x - 3
6x(x+1.5)-2(x+1.5)
(6x-2)(x+1.5)
2(3x-1)(x+1.5)

so we have :
[2(3x-1)(x+1.5)] / [x(-3x + 1)]

and you should know that (3x-1) / (-3x+1) = -1
so :

-2(x+1.5) / x

this is the simplified form

Answer 6

thank you so much!! you showed just enough work for me to understand how you did that that was great thank you

Answer 7

yw one more thing to say here is
6x^2 +7x - 3
do you know how i chose to split 7x into 9x-2x ?

Answer 8

so you could split it into the ( )

Answer 9

yes but how i knew to split it exacly to 9x-2x
and not 5x+2x for example

if you know why it's good if not ill explain