MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Division of an Expression by a Expression

Factorise: ...

Question

Factorise: $a^{2} + \frac{1}{a^{2}} + 3 - 2 a - \frac{2}{a}$

A

(a + \frac{1}{a} - 1) (a - \frac{1}{a} + 1)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

(a + \frac{1}{a} - 1) (a + \frac{1}{a} + 1)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

(a + \frac{1}{a} + 1) (a + \frac{1}{a} + 1)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

(a + \frac{1}{a} - 1) (a + \frac{1}{a} - 1)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $(a + \frac{1}{a} - 1) (a + \frac{1}{a} - 1)$
$a^{2} + \frac{1}{a^{2}} + 3 - 2 a - \frac{2}{a}$
$= a^{2} + \frac{1}{a^{2}} + 1 + 2 - 2 a - \frac{2}{a}$
$= {(a)}^{2} + {(\frac{1}{a})}^{2} + {(- 1)}^{2} + 2 \times a \times \frac{1}{a} + 2 \times a \times (- 1) + 2 \times \frac{1}{a} \times (- 1)$
$∵ {(a + b - c)}^{2} = a^{2} + b^{2} + c^{2} + 2 a b - 2 a c - 2 c b$
$= {(a + \frac{1}{a} - 1)}^{2} = (a + \frac{1}{a} - 1) (a + \frac{1}{a} - 1)$

Suggest Corrections

thumbs-up

0

Similar questions

\frac{a^{2} - 4}{a + 1} \times \frac{(a + 1) (a - 1)}{(a + 2)}

Q. Simplify the following expressions.

(\frac{a \sqrt{2}}{(1 + a^{2})^{- 1}} - \frac{2 \sqrt{2}}{a^{- 1}}) \frac{a^{- 3}}{1 - a^{- 2}}

lim n \to \infty n \sum a = 2 {sin}^{- 1} [\frac{\sqrt{(a^{2} + 2 a)} - \sqrt{(a - 1) (a + 1)}}{a (a + 1)}] = \frac{k π}{120},

then the value of

k

Q. Determine the value of

\frac{a^{2} - 4}{a + 1} \times \frac{(a - 1) (a + 1)}{a + 2}

.

x : | x + 1 | = | x | + a, a \neq \pm 1

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Division of an Expression by a Expression

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Division of an Expression by a Expression

Standard VIII Mathematics

Join BYJU'S Learning Program

CrossIcon