Question

Simplify the rational expression. State any excluded values. x-2/x^2+3x-10

Answer 1

you have to factor the denominator

x^2 + 3x - 10
do you know how to factor it ?

Answer 2

No can you show me how

Answer 3

ax^2 + bx + c

you have to split the 'b' into two terms say b1 and b2
ax^2 + b1x + b2x +c

your b1 and b2 have to satisfy the conditions :
b1 + b2 =2
and
b1 * b2 = a * c

in this case we can choose b1 to be 5 and b2 to be -2
so :
5 - 2 = 3
and 5*-2 = -10

Answer 4

then we will have x^2 + 5x - 2x - 10 in the denominator
now can you factor it ?

Answer 5

im trying to understand it

Answer 6

splitting 'b' is a method that will help you to eventually factor it ..
it is important to understand this method

Answer 7

How I describe factorization is we first look at the constant only. And we write down or think about all the numbers, when multiplied will give us this value.

Answer 8

So for -10 it's: -1,10 1,-10 2,-5 -2,5

Answer 9

Now we look at the coefficient of the middle term and think what pair of numbers when i add them will give me this coefficient

Answer 10

The coefficient is 3 so if we add the pair -2,5 we get 3

Answer 11

Now we know it must be in the form (x-2)(x+5) Does this help?

Answer 12

yes im still trying to work it though

Answer 13

After you factor the denominator it should look like this \[\frac{ x-2 }{ (x-2)(x+5) }\]Do you see anything that can be simplified from here?

Answer 14

My description of factoring is the same as @Coolsector 's just with more words

Answer 15

umm no?

Answer 16

cant you see a term that it is in the denominator and in the nominator ?

Answer 17

if you substitute x-2=y
\[\frac{ y }{ y(x+5) }\]Now what do you see?

Answer 18

x-2/x^2+3x-10\[\frac{ x - 2 }{ x^2 + 3x - 10 } = \frac{ x - 2 }{ (x - 2)(x + 5) } = \frac{ 1 }{ x + 5 }\]

Answer 19

How about "8"=x-2
\[\frac{ 8 }{ 8(x+5) }\]

Answer 20

plz don't give the answer @KKJ it helps them more to work through it

Answer 21

The major problem here is how to factorize the quadratic function

Answer 22

thats how i was working it out kkj but i was confused Thank you

Answer 23

Thanks guys!

Answer 24

yw

Answer 25

\[x^2- 36\] is difference of two squares

Answer 26

@kkj its on the new on i just posted not this one lol

Answer 27

\[\frac{ x^2-36 }{ 6 - x } = \frac{ (x - 6)(x + 6) }{ -1(x - 6) } = \frac{ x + 6 }{ -1 } = -x - 6\]

Answer 28

ty