What will be the simplified form of the rational expression $\frac{p (x)}{q (x)}, where p (x) = 81 x^{5} - 81 x and q (x) = (9 x^{2} + 9) (3 x + 3)$ ?
(A) 2x(x – 1) (2) 3x(x – 1) (3) 3(x – 1) (4) 3x(x + 1)

Question

What will be the simplified form of the rational expression p x q x
,   where   p x = 81   x 5 - 81 x   and  
q x = 9 x 2 + 9 3 x + 3 ?
(A) 2x(x – 1) (2) 3x(x
– 1) (3) 3(x – 1) (4) 3x(x +
1)

Sanjari Kalantri · Accepted Answer

Dear Student,

We have: px = 81x5 - 81x and qx = 9x2 + 93x + 3Now, px = 81x5 - 81x = 81xx4 - 1 = 81xx2 - 1x2 + 1 = 81xx + 1x - 1x2 + 1                 ∵ a2 - b2 = a + ba - band, qx = 9x2 + 93x + 3 = 9x2 + 1 × 3x + 1 = 27x2 + 1x + 1∴ Thus, pxqx = 81xx + 1x - 1x2 + 127x2 + 1x + 1 = 3xx - 1

What will be the simplified form of the rational expression p x q x , where p x = 81 x 5 - 81 x and q x = 9 x 2 + 9 3 x + 3 ? (A) 2x(x – 1) (2) 3x(x – 1) (3) 3(x – 1) (4) 3x(x + 1)

What will be the simplified form of the rational expression $\frac{p (x)}{q (x)}, where p (x) = 81 x^{5} - 81 x and q (x) = (9 x^{2} + 9) (3 x + 3)$ ?
(A) 2x(x – 1) (2) 3x(x – 1) (3) 3(x – 1) (4) 3x(x + 1)