If 2x - 3-x - 1x - 3 - a-x - 1 - b-x - 3- then a - b -

Explanation for the correct option: Find the value of 𝑎+𝑏:Given, 2x + 3/(x + 1)(x 3) = a/x + 1 + b/x 3⇒ 2x + 3/(x + 1)(x 3) = a(x 3) + b(x + 1)/(x + ...

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

Byju's Answer

Standard IX

Mathematics

Coefficients of a Polynomial

If 2x + 3/x +...

Question

If $\frac{2 x + 3}{(x + 1) (x - 3)} = \frac{a}{x + 1} + \frac{b}{x - 3}$ , then $a + b =$

$1$

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

$2$

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

$\frac{9}{4}$

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

None of these

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

Open in App

Solution

The correct option is B
$2$

Explanation for the correct option:
Find the value of $a + b$ :
Given, $\frac{2 x + 3}{(x + 1) (x - 3)} = \frac{a}{x + 1} + \frac{b}{x - 3}$
$\Rightarrow$ $\frac{2 x + 3}{(x + 1) (x - 3)} = \frac{a (x - 3) + b (x + 1)}{(x + 1) (x - 3)}$
$\Rightarrow$ $(2 x + 3) = a x - 3 a + b x + b$
$\Rightarrow$ $(2 x + 3) = (a + b) x - 3 a + b$
Step 2. Compare the coefficient of $x$ :
$\Rightarrow (a + b) = 2$
Hence, Option ‘B’ is Correct.

Suggest Corrections

Similar questions

Q. If

x^{3} - \frac{1}{x^{3}} = 14

, then

x - \frac{1}{x} =

(a) 5

(b) 4

(c) 3

(d) 2

Q. If x³ − 3x² + 3x − 7 = (x + 1) (ax² + bx + c), then a + b + c =

(a) 4

(b) 12

(c) −10

(d) 3

Q. If

\frac{x + 1}{x^{2} - p x + q} = \frac{A}{x - α} + \frac{B}{x - β}

, where

α

and

β

are the roots of

x^{2} - p x + q = 0

, then

\frac{A - B}{A + B} = \frac{p + 2}{\sqrt{p^{2} - 4 q}}

. If this is true enter 1, else enter 0.

Q. In a triangle ABC,if

A - B = 120^{\circ}

and

sin \frac{A}{2} sin \frac{B}{2} sin \frac{C}{2} = \frac{1}{32}

then the value of

8 cos C

Q. If A + B + C =

π

, then prove that,

s i n \frac{A}{2} + s i n \frac{B}{2} + s i n \frac{C}{2} = 1 + 4 s i n [\frac{π - A}{4}] s i n [\frac{π - B}{4}] s i n [\frac{π - C}{4}]

Join BYJU'S Learning Program

If 2x+3x+1(x-3)=ax+1+bx-3, then a+b=

The correct option is B 2Explanation for the correct option: Find the value of a+b:Given, 2x+3x+1(x-3)=ax+1+bx-3⇒ 2x+3x+1(x-3)=ax-3+bx+1x+1x-3⇒ 2x+3=ax-3a+bx+b⇒ 2x+3=a+bx-3a+bStep 2. Compare the coefficient of x:⇒(a+b)=2Hence, Option ‘B’ is Correct.

If $\frac{2 x + 3}{(x + 1) (x - 3)} = \frac{a}{x + 1} + \frac{b}{x - 3}$ , then $a + b =$