Question

Simplify the expression: x-4/x^2-49 - 1/x+7 all over x/x-7

Answer 1

hard to parse this one. maybe
\[\frac{\frac{x-4}{x^2-49}-\frac{1}{x+7}}{\frac{x}{x-7}}\]\]

Answer 2

thank you, yes that is how it should look.

Answer 3

ok then if i were you i would multply top and bottom of the big fraction by
\[\frac{x^2-49}{x^2-49}\] to clear the fractions

Answer 4

with the understanding that
\[x^2-49=(x+7)(x-7)\] so all the fractions will cancel and you will just get a numerator and denominator to combine like terms

Answer 5

i will write the steps if you like

Answer 6

that would help a lot, thanks. I'm kind of slow when it comes to this heh

Answer 7

ok so lets go real slow.

Answer 8

the denominator is
\[\frac{x}{x-7}\] so if you multiply it by \[(x+7)(x-7)\] the
\[x-7\] will cancel. you will get
\[\frac{x}{x-7}\times (x+7)(x-7)=x(x+7)\]

Answer 9

ok

Answer 10

so that will be our denominator. we are not done of course

Answer 11

now multiply the numerator by
\[(x+7)(x-7)=x^2-49\]

Answer 12

you get
\[(\frac{x-4}{x^2-49}-\frac{1}{x+7})\times (x+7)(x-7)\]

Answer 13

for the first term everything cancels. for the second term the
\[x+7\] cancels giving
\[x-4-1(x-7)\]

Answer 14

the parentheses are important because it is - the whole thing.

Answer 15

so now we have a fraction as
\[\frac{x-4-1(x-7)}{x(x+7)}\]

Answer 16

alright, I'm still with you :3

Answer 17

well we are essentially done. now it is just a matter of multiplying out and combining like terms. i get
\[
\frac{x-4-x+7}{x^2+7x}\] or
\[\frac{3}{x^2+7x}\]

Answer 18

yay =) I got that too~ Also, do you mind helping me understand one more? it's a bit easier I think

Answer 19

k

Answer 20

it's x/x+y-2xy/x^2-y^2+y/x-y

Answer 21

yikes

Answer 22

sorry, I don't know how to write it pretty like you.

Answer 23

\[\frac{x}{x+y}-\frac{2xy}{x^2-y^2}+\frac{y}{x-y}\]

Answer 24

yeah

Answer 25

use
\[x^2-y^2=(x+y)(x-y)\] as your common denominator.

Answer 26

you have to multiply the first one top and bottom by
\[x-y\] the middle one is fine as it is and the last one multiply top and bottom by
\[x+y\] that should give it to you

Answer 27

denominator will just be
\[x^2-y^2\] numerator will be

\[x(x-y)-2xy+y(x+y)\]

Answer 28

multiply out and combine like terms. i get
\[x^2-xy-2xy+xy+y^2\]
\[x^2-2xy+y^2\]
\[(x-y)(x-y)\] and i guess now you can cancel a
\[x-y\] from top and bottom to get
\[\frac{x-y}{x+y}\]

Answer 29

awesome! That made much more sense <3 I was trying to figure out where the 2 went lol. Thank you so much for your help, is there a way to give you super bonus points?