find x
x-5/x-2 = x-9/x-7
Method
(x-5)(x-7) = (x-9)(x-2)
x^2-12x+35 = x^2-11x-18
I get stuck here
help would be must appreciated
In this equation, we have:
(x-5)/(x-2) = (x-9)/(x-7)
To solve for x, we can multiply both sides of the equation by (x-2)(x-7) to eliminate the denominators. This is known as clearing the fractions.
So, we get:
(x-5)(x-7) = (x-9)(x-2)
Expanding both sides of the equation, we have:
x^2 - 7x - 5x + 35 = x^2 - 2x - 9x + 18
Combining like terms, we have:
x^2 - 12x + 35 = x^2 - 11x + 18
To continue solving for x, we can simplify the equation by subtracting x^2 from both sides:
-12x + 35 = -11x + 18
Next, we can subtract 18 from both sides:
-12x + 35 - 18 = -11x
-12x + 17 = -11x
To isolate the variable x, we can subtract -11x from both sides:
-12x + 17 - (-11x) = 0
-12x + 11x + 17 = 0
Simplifying further:
-1x + 17 = 0
To solve for x, we can subtract 17 from both sides:
-1x = -17
Finally, divide both sides by -1 to solve for x:
x = 17
So, the solution to the equation is x = 17.