Can anyone help me with this question?
2/(-1+x)+1/(x-2)=2/(1-x)
Thanks =]
Did you realize that 2/(1-x) is the same as -2/(x-1) ?
so we rewrite it as
2/(x-1) + 1/(x-2 = -2/(x-1)
1/(x-2) = -4/(x-1)
cross-multiply
x-1 = -4x + 8
5x = 9
x = 9/5
Thank you so much for the help ^^
Of course, I can help you with that! The given equation is:
2/(-1+x) + 1/(x-2) = 2/(1-x)
To solve this equation, we need to find the value(s) of x that satisfy the equation. Let's go step by step:
Step 1: Simplify the denominators
Multiply the first fraction by (x-2)/(x-2) to simplify the denominator -1+x:
-2/(x-2+x-2) + 1/(x-2) = 2/(1-x)
This simplifies to:
-2/(2x-4) + 1/(x-2) = 2/(1-x)
Step 2: Combine fractions with common denominators
To combine fractions, we need a common denominator. In this case, the common denominator is (2x-4)(x-2)(1-x).
Multiply each fraction by the necessary factors to get the common denominator:
(-2)(1-x)/(2x-4)(x-2)(1-x) + (1)(2x-4)/(2x-4)(x-2)(1-x) = (2)(x-2)/(2x-4)(x-2)(1-x)
After simplifying, we have:
(-2 + 2x - 4)/(2x-4)(x-2)(1-x) + (2x-4)/(2x-4)(x-2)(1-x) = (2x-4)/(2x-4)(x-2)(1-x)
Step 3: Combine like terms
Combine the numerators on the left side of the equation:
(2x - 6)/(2x-4)(x-2)(1-x) = (2x-4)/(2x-4)(x-2)(1-x)
Step 4: Cancel common factors
Notice that (2x-4) is a common factor in both the numerator and denominator on both sides of the equation. Canceling these factors, we get:
(2x - 6)/(x-2)(1-x) = 1/(x-2)(1-x)
Step 5: Cross-multiply
Cross-multiplication means multiplying the numerator of one fraction by the denominator of the other fraction.
We have:
(2x - 6) = (x-2)(1-x)/(x-2)(1-x)
Now, we have an equation without fractions.
Step 6: Simplify and solve
Distribute the (x-2) and (1-x) on the right side:
(2x - 6) = -(x-2)
Simplify further:
2x - 6 = -x + 2
Now, solve for x:
2x + x = 2 + 6
3x = 8
x = 8/3
So, the solution to the given equation is x = 8/3.