Solve the following equation using the method | vedclass

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

Question

(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

Vedclass · Accepted Answer

$\{-\sqrt{5}, \sqrt{5}\}$

Vedclass · Answer

(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 $\{-\sqrt{5}, \sqrt{5}\}$.

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

The roots of the quadratic equation $3x^2 - 4x + 1 = 0$ are:

Find two consecutive positive integers,the sum of whose squares is $365$.

Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?

Find the roots of the following quadratic equation by the method of completing the square: $m^{2}-18m+81=0$

The altitude of a right triangle is $7 \, cm$ less than its base. If the hypotenuse is $13 \, cm$,find the other two sides.

Vedclass Test Series

Exam Paper Generator

Online Exam Module