## Chiomatn93 3 years ago solve for x.

1. Chiomatn93

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2. Australopithecus

or you could just go (x-3)(x-7) = (x-5)(x+2) + (x-5)

3. maheshmeghwal9

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4. Australopithecus

now expand and simplify

5. maheshmeghwal9

Now Simplify & solve. Can you do it now?

6. UnkleRhaukus

$\frac{x-3}{x-5}=\frac{x+2}{x-7}+1$ $\frac{x-3}{x-5}-\frac{x+2}{x-7}-1=0$ $=\frac{(x-7)(x-3)}{(x-7)(x-5)}-\frac{(x-5)(x+2)}{(x-5)(x-7)}-\frac{(x-5)(x-7)}{(x-5)(x-7)}$ $=\frac{(x-7)(x-3)-(x-5)(x+2)-(x-5)(x-7)}{(x-7)(x-5)}$

7. Chiomatn93

solve for x!!!

8. Australopithecus

What are you having problems with exactly? do you know how to simplify equations at all?

9. Australopithecus

(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

10. Australopithecus

I have no idea what the other people are doing in this problem :l

11. sheg

have u understood how to solve this problem???

12. Australopithecus

x^(2) - 10x + 21 = x^(2) - 3x - 10 = -10x + 3x = -10 - 21 = -7x = -31 x = -31/-7 = x = 31/7

13. Australopithecus

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

14. Chiomatn93

okay thanks so much lol..

15. Australopithecus

do you have any idea how I solved this? If you want me to show you how I can.

16. Chiomatn93

yes please... im not the sharpest knife in the drawer when it comes to mathematics!

17. Australopithecus

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

18. Australopithecus

19. Australopithecus

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

20. Australopithecus

collect all x terms on one side of the equation and move all plain numbers on the other side of the equation

21. Australopithecus

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

22. Chiomatn93

alright thanks a bunch!

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