Help check my working

[misty nimbus]

To partial fraction decompose $ \frac{-10x-5}{x^2+x-42} $ first I factored the denominator (x-6)(x+7) then $\frac{A}{x-6}+\frac{B}{x-7}$ then I made $\frac{A}{x-6}+\frac{B}{x-7}=\frac{-10x-5}{(x-6)(x+7)}$ then I multiplied both sides by (x-6)(x+7) to get rid of fractions $A(x-6)+B(x+7)=-10x-5$ to solve for A, I made x=-7 so that B would cancel $A(-7-6)+B(-7+7)=-10(-7)-5$ then I simplified $-13A=65$ then I divided both sides by -13, A=-5. Then I made x=6 to get rid of A to solve for B, $A(6-6)+B(6+7)=-10(6)-5$, then simplify, 13B=-65 then divide both sides by 13, B=-5. So then plug all that into $\frac{A}{x-6}+\frac{B}{x-7}$, $\frac{5}{x-6}+\frac{-5}{x-7}$, But khan academy says I got the answer incorrect, where did I go wrong?

[cursive onyx]

kangaroo rat

[slow robin]

A(x-7) + B(x-6)

you don’t multiply by the denominator of the original fraction

you cross multiply so there is a single common denominator across the whole thing

talking about the 4th line btw

@misty nimbus

[misty nimbus]

Wdym?

I kinda don’t get what your saying

[slow robin]

ayo wait i’m being stupid

i never realised you could do it like that

,w partical fraction (-10x-5)/(x^2+x-42)

[slow robin]

ignore what i said before
your final lines are wrong

$\frac{\left(-5\right)}{x-6}+\frac{\left(-5\right)}{x+7}$

[cursive onyx]

Jamesss

[slow robin]

you have just done some goofy stuff when substituting

[misty nimbus]

like what?

[slow robin]

you got the denominator as (x-7) and it’s (x+7) and you substituted 5 into A instead of -5

[slow robin]

here is the corrected line

[misty nimbus]

Oh so just wired mistakes

thanks

[misty nimbus]

@slow robin Could you please help with this too. Where did I go wrong in my working for $\frac{7x-33}{x^2-8x-9}$? first factor the denominator (x+1)(x-9) then $\frac{A}{x+1}+\frac{B}{x-9}$. Next you have to solve for $\frac{A}{x+1}+\frac{B}{x-9}=\frac{7x-33}{(x+1)(x-9)}$.Next multiply both sides by (x+1)(x-9), A(x-9)+B(x+1)=7x-33. Then to solve for B make A=0 by making x=9, so plug that in then simplify 10B=-96, divide both sides by 10, B=-9$\frac{3}{5}$. Next solve for A by making B=0 by making x=-1, so plug that in and simplify, -10A=-40, so then divide both sides by -10 and that gives you A=-4. So finally the fraction decomposed is $\frac{-4}{x+1}+\frac{-9\frac{3}{5}}{x-9}$

[cursive onyx]

kangaroo rat

[slow robin]

,w partial fraction (7x-33)/(x^2-8x-9)

[slow robin]

,w 7(9)-33

[slow robin]

@misty nimbus U got b wrong

also a is positive -40/-10 = 4

[misty nimbus]

how should I do b (with the same strategy)?

[misty nimbus]

@slow robin can you show me your working to solve for b with the same strategy?

[slow robin]

i’m drunk af btw so make sure everything. i say makes sense

[slow robin]

what kind of physics is this

il this isn't related to ur question but like

this is stressing me out

nvm

his is

mathematics

WTF

whatever

$7x-33=A\left(x-9\right)+B\left(x+1\right)$\\$\text{let x = 9 } 10B = 7(-9)-33 \implies B= \frac{\frac{7(9)-33}{10}=3$\\$\text{let x=-1 } A(-10)=7(-1)-33 \implies A=4$

[cursive onyx]

Jamesss
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[slow robin]

oh dman

when not drunk o will do avon

again

is this a level math

wtf us thsi

so difficult for what

but basically you did the 7x -33 part wrong

sign error

not difficult just technical

[misty nimbus]

@slow robin huh?

[slow robin]

sry i was a litrle

out of it

what grade ru in

i wanna see if ill have to kms anytime soon

[misty nimbus]

oh ok

[slow robin]

marh us so hard

[misty nimbus]

lol sometimes

you will be fine

[misty nimbus]

English only lol

[slow robin]

do u mind

telling me

what grade ur in

like af school

or if ur in uni

cuz i wanna figure out when i have to do this

[misty nimbus]

10th nearly 11th

you probably have a while

what about u?

[slow robin]

rip kangaroo

$7x-33=A\left(x-9\right)+B\left(x+1\right)$\\$\text{let x = 9 } 10B = 7(-9)-33 \implies B= \frac{7(9)-33}{10}=3$\\$\text{let x=-1 } A(-10)=7(-1)-33 \implies A=4$

[misty nimbus]

why?

[misty nimbus]

and there is problem here

[slow robin]

drunk me put a \frac\frac down

oml where did my spaces go

[cursive onyx]

Jamesss

[slow robin]

there

[misty nimbus]

ok

[misty nimbus]

why didn't you simplify earlier?

[slow robin]

in 10th

theres no way

😭

imma kms

ong

[slow robin]

simplify what

[misty nimbus]

simplify $7(9)$

[cursive onyx]

kangaroo rat

[cedar crest]

63

jk

7 times the (square root of 9) squared

[slow robin]

it simplifies in the next part

just lazy

[misty nimbus]

oh lol i just realized it doesn't change

[misty nimbus]

lol

[cedar crest]

its fax tho

[misty nimbus]

ye

[misty nimbus]

ok thanks