a(x-2)+b(x-4)=x+2 find the values of a and b?

let x-2=0
x=2

a(2-2)+b(2-4)=2+2
-2b=4
b=-2 answer

to find the value of a let x-4=0 x=4
a(4-2)+b(4-4)=4+2
2a=6
a=3 answer

ax - 2a + bx - 4b = x + 2
(a + b)x - 2(a + 2b) = x + 2

a + b = 1
-2a - 4b = 2

4a + 4b = 4
-2a - 4b = 2------ADD

2a = 6
a = 3

3 + b = 1
b = - 2

a = 3 , b = - 2

a(x - 2) + b(x - 4) = x + 2
ax - 2a + bx - 4b = x + 2
ax + bx - 2a - 4b = x + 2
x(a + b) - (2a + 4b) = x + 2

x(a + b) = x
a + b = x/x
a + b = 1
a = 1 - b

-(2a + 4b) = 2
-2a - 4b = 2
-2(1 - b) - 4b = 2
-2 + 2b - 4b = 2
-2b = 2 + 2
b = 4/-2
b = -2

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

∴ a = 3 , b = -2

a = 3
b = -2

This is solved by comparing left hand side with right hand side.
You'll get:

Equation 1:

ax + bx = x
Therefore, a+b =1 ... (1)

Equation 2:
-2a -4b = 2 ... (2)

Solving both equations simultaneously, you'll get the answer mentioned above:

a+b =1 ... (1)
-2a - 4b = 2 ... (2)

yuck. Good luck

let x = 4 -->2a = 6 --> a = 3

let x = 2 ---> -2b = 4 ---> b = -2