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or you could just go (x-3)(x-7) = (x-5)(x+2) + (x-5)
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now expand and simplify
Now Simplify & solve. Can you do it now?
\[\frac{x-3}{x-5}=\frac{x+2}{x-7}+1\] \[\frac{x-3}{x-5}-\frac{x+2}{x-7}-1=0\] \[=\frac{(x-7)(x-3)}{(x-7)(x-5)}-\frac{(x-5)(x+2)}{(x-5)(x-7)}-\frac{(x-5)(x-7)}{(x-5)(x-7)}\] \[=\frac{(x-7)(x-3)-(x-5)(x+2)-(x-5)(x-7)}{(x-7)(x-5)}\]
solve for x!!!
What are you having problems with exactly? do you know how to simplify equations at all?
(x-3)(x-7) = (x-5)(x+2) + (x-5) = x^(2) - 10x + 21 = x^(2) - 3x - 10 = Im sure you can solve it from here but if you dont know how I got (x-3)(x-7) = (x-5)(x+2) + (x-5) from your original problem then say so
I have no idea what the other people are doing in this problem :l
have u understood how to solve this problem???
x^(2) - 10x + 21 = x^(2) - 3x - 10 = -10x + 3x = -10 - 21 = -7x = -31 x = -31/-7 = x = 31/7
that is your answer the rest of the people who attempted this problem need a refresher on algebra and solving equations or they just did things the long way
okay thanks so much lol..
do you have any idea how I solved this? If you want me to show you how I can.
yes please... im not the sharpest knife in the drawer when it comes to mathematics!
well first you always want to bring all x terms into the numerator so to do this I multiplied both sides of the equation by (x-5) and (x-7) so (x-3)(x-5)(x-7)/(x-5) = (1 + (x+2)/(x-7)) * (x-5)(x-7) = (x-3)(x-7)(1) = (x-5)(x-7) + (x-5)(x-7)(x+2)/(x-7) = (x-3)(x-7) = (x-5)(x-7) + (x-5)(x+2)(1) = (x-5)(x-7) + (x-5)(x-7)(x+2) = (x-5)(x-7) + (x-5)(x+2) = Now expand everything Looks like I made a mistake :S
in my previous answer
ugh my brain it is dead. (x-3)(x-5)(x-7)/(x-5) = (1 + (x+2)/(x-7)) * (x-5)(x-7) = (x-3)(x-7)(1) = (x-5)(x-7) + (x-5)(x-7)(x+2)/(x-7) = (x-3)(x-7) = (x-5)(x-7) + (x-5)(x+2)(1) = (x-3)(x-7) = (x-5)(x-7) + (x-5)(x+2) Now expand and simplify to get the answer
collect all x terms on one side of the equation and move all plain numbers on the other side of the equation
this problem is quadratic so yeah there are two solutions https://www.wolframalpha.com/input/?i=%28x-3%29%28x-7%29+%3D+%28x-5%29%28x-7%29+%2B+%28x-5%29%28x%2B2%29
alright thanks a bunch!

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