Question

Simplify the rational expression. State any excluded values.
x^2-36/42x-7x^2

Answer 1

It would be (x-6)(x+6) but idk where to go from there

Answer 2

so you already knows what is x^2-36 (from the previous question)

with 42x-7x^2
you can do something .. like taking out 7x .. what will you have ?

Answer 3

x - 2 / x^2 + 3x - 10
x^2 - 36 / 6 - x
x^2 - 36 / 42 x - 7x^2

Answer 4

how do you take out 7x?

Answer 5

42x-7x^2 = 7x ( 6 - x )
(you take 7x out and what inside ( ) is every term divided by 7x )

Answer 6

\[42x - 7x^2\] has some terms common to them
Can you notice it?

Answer 7

the x

Answer 8

That is true

Answer 9

Consider 42 and 7

Answer 10

Can one go into the other?

Answer 11

yes

Answer 12

What is that?

Answer 13

6

Answer 14

So 7 can go to 42 6 times

Answer 15

yes

Answer 16

remember x was also common to them
This makes it 7x

Answer 17

\[\frac{ x^2-36 }{ 42x - 7x^2 } = \frac{ (x + 6)(x - 6) }{ 7x(6 - x) }\]

Answer 18

Can you continue from here?

Answer 19

\[\frac{ x^2-36 }{ 42x - 7x^2 } = \frac{ (x + 6)(x - 6) }{ (7x)(-1)(x - 6) }\]

Answer 20

so the answer would be x-6/7x

Answer 21

is it

Answer 22

\[\frac{ x + 6 }{ -7x }\]

Answer 23

or \[\frac{ -x - 6 }{ 7x }\]

Answer 24

ty