Question 277164
{{{(8x-3)/(2x^2-x)}}} = {{{(8x-3)/x(2x-1)}}}
Write the given expression as a sum using A & B
{{{(8x-3)/x(2x-1)}}} = {{{A/x}}} + {{{B/(2x-1)}}}
:
Simplify by multipling each side by the LCD, x(2x-1)
x(2x-1)*{{{(8x-3)/x(2x-1)}}} = x(2x-1)*{{{A/x}}} + x(2x-1)*({{{B/(2x-1)}}}
Results
8x - 3 = A(2x-1) + Bx
:
8x - 3 = A2x - A + Bx
:
8x - 3 = x(2A + B) - A
The coefficient on one side = the coefficient on the other side
2A + B = 8
the constant on one side = the constant on the other side
-A = -3
A = 3
Substitute 3 for A and find B
2(3) + B = 8
B = 8 - 6
B = 2
So we have
{{{(8x-3)/x(2x-1)}}} = {{{3/x}}} + {{{2/(2x-1)}}}