Solve the solution (x - 5) / (x - 8) = (x + 1) / (x - 5)?

(x - 5) / (x - 8) = (x + 1) / (x - 5)
-> (x-5)^2 = (x+1)(x-8)
-> x^2 -10x +25 = x^2 -7x -8
->3x=33 -> x = 11

(x - 5)/(x - 8) = (x + 1)/(x - 5)
(x - 5)² = (x + 1)(x - 8)
x² - 5x - 5x + 25 = x² - 8x + x - 8
x² - 10x + 25 = x² - 7x - 8
3x = 33
x = 11

Answer: x = 11

Proof:
(11 - 5)/(11 - 8) = (11 + 1)/(11 - 5)
6/3 = 12/6
2 = 2

cross multiply
(x-5) (x-5)=(x-8) (x+1)
x^2 + 5^2 - 2(5x)= x^2 -8 -8x +x
x^2 gets cancelled off on both sides
25 -10x +8x +8 -x = 0
-3x =-33
x=11
sorry bout the earlier answer!!!!

X 5 X 8

(x - 5)² = (x + 1)(x - 8)
x² - 10 x + 25 = x² - 7 x - 8
33 = 3 x
x = 11

(x - 5)/(x - 8) = (x + 1)/(x - 5)
(x - 5)(x - 5)/(x - 8)(x - 5) = (x + 1)(x - 8)/(x - 5)(x - 8)
(x^2 - 10x + 25)/(x^2 - 13x + 40) = (x^2 - 7x - 8)/(x^2 - 13x + 40)
x^2 - 10x + 25 = x^2 - 7x - 8
x^2 - x^2 - 10x + 7x = -25 - 8
-3x = -33
x = -33/-3
x = 11

(x - 5)/(x - 8) = (x + 1)/(x - 5)

(x - 5)^2 = (x + 1)(x - 8)
x^2 - 5x - 5x + 25 = x^2 - 8x + x - 8
x^2 - 10x + 25 = x^2 - 7x - 8
3x = 33
x = 11

(x - 5) / (x - 8) = (x + 1) / (x - 5)
(x-5)^2
(x-5)(x-5)
x^2 -5x - 5x +25
x^2 - 10x + 25
(x-8)(x+1)
x^2+x-8x-8
x^2+7x-8
x^2-10x+25 = x^2+7x-8
-x^2 -x^2
-10x+25 = 7x-8
+10x +10x
25 = 17x-8
+ 8 +8
34 = 17x
/17 /17
2 = x

X=11/use cross multiplication.

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x^2-10x+25=x^2-7x-8
x=11