MyQuestionIcon

1

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

Addition of Rational Expressions

Which rationa...

Question

Which rational expression should be subtracted from $\frac{4 x^{3} - 7 x^{2} + 5}{2 x - 1}$ to get $2 x^{2} - 5 x + 1$ ?

A

\frac{5 x^{2} - 7 x + 6}{2 x - 1}

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

B

\frac{5 x^{2} + 7 x + 6}{2 x - 1}

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

C

\frac{5 x^{2} - 7 x + 6}{2 x + 1}

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

D

None of these

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

Open in App

Solution

The correct option is A $\frac{5 x^{2} - 7 x + 6}{2 x - 1}$
Let the rational expression be $A$ that must be subtracted from $\frac{4 x^{3} - 7 x^{2} + 5}{2 x - 1}$ to get $2 x^{2} - 5 x + 1$ , therefore, we have:

$\frac{4 x^{3} - 7 x^{2} + 5}{2 x - 1} - A = 2 x^{2} - 5 x + 1 \Rightarrow A = \frac{4 x^{3} - 7 x^{2} + 5}{2 x - 1} - \frac{2 x^{2} - 5 x + 1}{1} \Rightarrow A = \frac{(4 x^{3} - 7 x^{2} + 5) - (2 x - 1) (2 x^{2} - 5 x + 1)}{2 x - 1} (T a k i n g L C M) \Rightarrow A = \frac{(4 x^{3} - 7 x^{2} + 5) - (4 x^{3} - 10 x^{2} + 2 x - 2 x^{2} + 5 x - 1)}{2 x - 1}$
$\Rightarrow A = \frac{(4 x^{3} - 7 x^{2} + 5) - (4 x^{3} - 12 x^{2} + 7 x - 1)}{2 x - 1} \Rightarrow A = \frac{4 x^{3} - 7 x^{2} + 5 - 4 x^{3} + 12 x^{2} - 7 x + 1}{2 x - 1} \Rightarrow A = \frac{5 x^{2} - 7 x + 6}{2 x - 1}$

Hence, $\frac{5 x^{2} - 7 x + 6}{2 x - 1}$ should be subtracted from $\frac{4 x^{3} - 7 x^{2} + 5}{2 x - 1}$ to get $2 x^{2} - 5 x + 1$ .

Suggest Corrections

thumbs-up

0

Similar questions

Q. Subtract the sum of

({5 x}^{2} - 7 x + 4)

(2 x - {5 x}^{3} + 1)

({3 x}^{2} - 1 + 5 x)

.

Q. What must be added to 5x³ − 2x² + 6x + 7 to make the sum x³ + 3x² − x + 1?
(a) 4x³ − 5x² + 7x + 6
(b) −4x³ + 5x² − 7x − 6
(c) 4x³ + 5x² − 7x + 6
(d) none of these

Q. What must be subtracted from

x^{4} + 4 x^{2} - 3 x + 7

3 x^{3} - x^{2} + 2 x + 1

?

x^{4} - 3 x^{3} + 5 x^{2} - 5 x + 6

5 x^{2} - 7 x + 3, - 8 x^{2} + 2 x - 5

7 x^{2} - x - 2

\frac{1}{2} x - 2 \sqrt{5} x^{2} + \frac{1}{\sqrt{5}} x^{3}

\frac{3}{2} x - 4 \sqrt{5} x^{2} + \frac{1}{\sqrt{5}} x^{3}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Adaptive Q28

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Addition of Rational Expressions

Standard X Mathematics

Join BYJU'S Learning Program

CrossIcon