2/x-1 +3/x+2=2?

Question

solve and verify

Answer 1

2/x-1 +3/x+2=2

2-1x/x + 3+2x/x=2

2-1x+3+2x=2x

5+1x=2x

x=5

2/(5)-1 + 3/(5)+2 =2

Answer 2

You need a common denominator before combining the rational expressions. Since x - 1 and x + 2 are both simplified and can't be factored, just multiply each by 'the other.' Multiply the 2/( x-1) by (x+ 2)/(x + 2) and muliply the3/(x + 2) by (x -1)/(x - 1). Remember to multiply the 2 on the other side by both.

So, you'll get:
2(x + 2) / (x - 1)(x + 2) + 3(x - 1) / (x - 1)(x + 2) =

2(x - 1)(x + 2) / (x - 1)(x + 2)

Now, the denominators are all equal, so you can look at just the numerators:
2(x + 2) + 3(x - 1) = 2(x - 1)(x + 2)

Just distribute, expand, and simplify. Then you should be able to solve for x.

Answer 3

(2/(x - 1)) + (3/(x + 2)) = 2

Multiply everything by (x - 1)(x + 2)

2(x + 2) + 3(x - 1) = 2(x - 1)(x + 2)
2x + 4 + 3x - 3 = 2(x^2 + 2x - x - 2)
5x + 1 = 2(x^2 + x - 2)
5x + 1 = 2x^2 + 2x - 4
2x^2 - 3x - 5 = 0

x = (-b ± sqrt(b^2 - 4ac))/(2a)

x = (-(-3) ± sqrt((-3)^2 - 4(2)(-5)))/(2(2))
x = (3 ± sqrt(9 + 40))/4
x = (3 ± sqrt(49))/4
x = (3 ± 7)/4
x = (10/4) or (-4/4)
x = (5/2) or -1

ANS : x = -1 or 2.5

Answer 4

they way you have it written it would be
2/x -1 + 3/x +2 = 2
add one to both sides and subtract two from both sides
2/x +3/x = 2+1-2
2/x+3/x = 1
5/x = 1
1/5(5/x=1)
x=1/5
if it is 2/(x-1) you need to use parenthesis
hope it helps

Answer 5

2/(x-1) +3/x+2=2 multiply by (x+2)(x-1)
2(x+2)+3(x-1)=2(x+2)(x-1)
2x+4+3x-3=2(x^2+x-2)
5x+1=2x^2+2x-4
2x^2-3x-5=0
(2x-5)(x+1)=0
2x-5=0
x=2.5=5/2

x+1=0
x=-1

check
2/(-1-1)+3/(-1+2)=2
-1+3=2

2/(2.5-1)+3/(2.5+2)=2
2/1.5+3/4.5=2
6/4.5+3/4.5=2
9/4.5=2