Question

Help with this?

Answer 1

So my answer is x^2 + 3x - 10 is that right?

Answer 2

i get + 10 on top:

it can be simplified further. debatable if its even"simpler"

\[\frac{ x^2 + 3x + 10 }{ x^2 + x - 6 } = \frac{ (x^2 + x - 6) + 2x + 16 }{ x^2 + x - 6 } = 1 + \frac{ 2x+16 }{ x^2 + 6 - 6 } = 1 + \frac{ 2(x+8) }{ (x-2)(x+3) }\]

Answer 3

numerator is 2(x + 8). denom is factorized original

Answer 4

How did you get +10? Can you show me what you did starting from the beginning?

Answer 5

\(\large \frac{2x}{x-2} - \frac{x+5}{x+3}\)

Answer 6

first you need to make the denominators same,

Answer 7

I did, I multiplied the left by (x + 3) and the right by (x - 2)

Answer 8

\(\large \frac{2x}{x-2} \color{red}{\times\frac{x+3}{x+3}} - \frac{x+5}{x+3} \color{red}{\times\frac{x-2}{x-2}}\)

Answer 9

So I had
\[2x( x + 3)/ (x - 2)(x + 3)\] and \[(x + 5)(x - 2)/(x - 2)(x - 3)\]

Answer 10

I don't know how to get it into the format you had where they're right under each other lol

Answer 11

\(\large \frac{2x}{x-2} \color{red}{\times\frac{x+3}{x+3}} - \frac{x+5}{x+3} \color{red}{\times\frac{x-2}{x-2}}\)


\(\large \frac{2x(x+3)}{(x-2)(x+3)} - \frac{(x+5)(x-2)}{(x-2)(x+3)} \)

Answer 12

:) now bottoms are same
so simply subtract the tops

Answer 13

Then I simplified it to get..\[(2x^2 + 6x) - (x^2 + 3x - 10)\]

Answer 14

who ate the bottom ?

Answer 15

no one haha, but since we have like terms I just subtracted the top and added the bottom later so its

\[x^2 + 3x - 10/(x - 2)(x + 3)\]

Answer 16

everything looks fine except, that -10

Answer 17

outside there is -
so --10 =+10

Answer 18

Ohh I see, that's where I Messed up

Answer 19

good ! other than that ur work is great !

Answer 20

Thank you! Can we do another one?

Answer 21

sure :)
since they want u simplify, expand the bottom and give them ok