Question

What is the simplified form of x plus 2 over x squared minus 3x minus 10 • x minus 3 over x squared plus x minus 12 ?

1 over the quantity x minus 3 times the quantity x plus 4
1 over the quantity x minus 3 times the quantity x plus 2
1 over the quantity x plus 4 times the quantity x minus 5
1 over the quantity x plus 2 times the quantity x minus 5

Answer 1

\[\frac{ x + 2 }{ x^2 - 3x - 10 } \times \frac{ x - 3 }{ x^2 + x -12 }\]

Answer 2

@iGreen do i flip the 2nd fraction then horizontally multiply ?

Answer 3

No, that was for division..you can horizontally multiply now.

Answer 4

oh okay

Answer 5

quick question when we horizontally multipl would the numerator be x^2 + 2 -3 or x+ 2 x- 3?

Answer 6

None.. \(\sf (x+2)(x-3)\)

x * x = ?
x * -3 = ?
2 * x = ?
2 * -3 = ?

Answer 7

x^2
-3x
2
-6

Answer 8

Actually, first we cancel the common factors.

Answer 9

for the denominator
?

Answer 10

For the 2nd fraction

Answer 11

1st*

Answer 12

Factor \(\sf x^2 - 3x - 10\) from the numerator..tell me what you get.

Answer 13

Can you do that?

Answer 14

is it x/ x^2 - 3x -5

Answer 15

No..

Answer 16

Can you factor \(\sf x^2 - 3x - 10\)?

Answer 17

oh yeah give me sec

Answer 18

Okay

Answer 19

(x + 2) (x - 5)

Answer 20

Yes, so we have: \(\sf \dfrac{x+2}{(x-5)(x+2)} \times \dfrac{x-3}{x^2+x-12}\)

The x + 2's cancel out, giving us:

\(\sf \dfrac{\cancel{x+2}}{(x-5)(\cancel{x+2})} \times \dfrac{x-3}{x^2+x-12}\)

\(\sf \dfrac{1}{(x-5)} \times \dfrac{x-3}{x^2+x-12}\)

Answer 21

Now we multiply horizontally..but first factor \(\sf x^2 + x - 12\).

Answer 22

(x - 3) (x + 4)

Answer 23

but it would be \[\frac{ 1 }{ (x - 5) } \times \frac{ 1 } { ( x + 4)}\]

Answer 24

Yes..which gives us:

\(\sf \dfrac{1}{(x-5)(x+4)}\)

Answer 25

@shinebrightlikeadimon

Answer 26

okay thanks so much for some reason i lost connection thats why im replying late