Question

(2x+1)/ 4x3+4x2-x-1​

Answer 1

Answer:

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

Step-by-step explanation:

we have, (2x+1)/(4x³+4x²-x-1)

if we take, (2x+1) is a root of (4x³+4x²-x-1) because when we take,

2x+1 = 0

x = -1/2

and it satisfy the eq. 4x³+4x²-x-1 = 0

so, after that on dividing this eq. by 2x+1 it gives the quotient 2x²+x-1

so, eq. (4x³+4x²-x-1) = (2x+1)(2x²+x-1)

we can write as,

= (2x+1)/(2x+1)(2x²+x-1)

= 1/(2x²+x-1)

= 1/(2x²+2x-x-1)

= 1/[2x(x+1)-(x+1)]

= 1/[(2x-1)(x+1)] ....ans.