(B) Given equation: $\frac{x+1}{x-1} - \frac{x-1}{x+1} = \frac{5}{x}$Taking $LCM$ on the left side: $\frac{(x+1)^2 - (x-1)^2}{(x-1)(x+1)} = \frac{5}{x

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(B) Given equation: $\frac{x+1}{x-1} - \frac{x-1}{x+1} = \frac{5}{x}$Taking $LCM$ on the left side: $\frac{(x+1)^2 - (x-1)^2}{(x-1)(x+1)} = \frac{5}{x}$Simplify the numerator: $(x^2 + 2x + 1) - (x^2 - 2x + 1) = 4x$Simplify the denominator: $(x-1)(x+1) = x^2 - 1$So,$\frac{4x}{x^2 - 1} = \frac{5}{x}$Cross-multiply: $4x^2 = 5(x^2 - 1)$$4x^2 = 5x^2 - 5$$x^2 = 5$$x = \pm\sqrt{5}$Thus,the solution set is $\{-\sqrt{5}, \sqrt{5}\}$.

Class 10 Mathematics Quadratic Equations Mix Examples - Quadratic Equations

Medium

Solve the following equation using the method of factorization and write its solution set: $\frac{x+1}{x-1} - \frac{x-1}{x+1} = \frac{5}{x}$

A
$\{\frac{2}{5}, \frac{3}{5}\}$
B
$\{-\sqrt{5}, \sqrt{5}\}$
C
$\{-\sqrt{7}, \sqrt{13}\}$
D
$\{-\sqrt{2}, \sqrt{4}\}$

Explore More

Browse All

Question Bank

All Subjects

Class 10 Questions

Class 10

Mathematics Questions

Chapter

Quadratic Equations

Subtopic

Mix Examples - Quadratic Equations

At $t$ minutes past $2\, pm$, the time needed by the minute hand of a clock to show $3\, pm$ was found to be $3\, minutes$ less than $\frac{t^{2}}{4}$ $minutes$. Find $t$.

Medium

View Solution

If both the roots of $25x^{2} - x(m - 2) - 1 = 0$ are opposite,then $m = \ldots$

Medium

View Solution

The roots of a quadratic equation $x^{2} = 49$ are ..... .

Easy

View Solution

Which constant must be added and subtracted to solve the quadratic equation $9x^{2} + \frac{3}{4}x - \sqrt{2} = 0$ by the method of completing the square?

Easy

View Solution

$A$ two-digit number is such that the product of its digits is $10$. When $27$ is added to the original number,the new number obtained is the same as the number obtained by interchanging the digits of the original number. Determine the number.

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

Solve the following equation using the method of factorization and write its solution set: $\frac{x+1}{x-1} - \frac{x-1}{x+1} = \frac{5}{x}$

Similar Questions

At $t$ minutes past $2\, pm$, the time needed by the minute hand of a clock to show $3\, pm$ was found to be $3\, minutes$ less than $\frac{t^{2}}{4}$ $minutes$. Find $t$.

If both the roots of $25x^{2} - x(m - 2) - 1 = 0$ are opposite,then $m = \ldots$

The roots of a quadratic equation $x^{2} = 49$ are ..... .

Which constant must be added and subtracted to solve the quadratic equation $9x^{2} + \frac{3}{4}x - \sqrt{2} = 0$ by the method of completing the square?

$A$ two-digit number is such that the product of its digits is $10$. When $27$ is added to the original number,the new number obtained is the same as the number obtained by interchanging the digits of the original number. Determine the number.

Vedclass Test Series

Exam Paper Generator

Online Exam Module