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: $\frac{1}{x-3}-\frac{1}{x+5}=\frac{1}{6}$Taking the common denominator on the left side:$\frac{(x+5)-(x-3)}{(x-3)(x+5)}=\frac{1}{6

Vedclass · Accepted Answer

$-9$ and $7$

Vedclass · Answer

(B) Given equation: $\frac{1}{x-3}-\frac{1}{x+5}=\frac{1}{6}$Taking the common denominator on the left side:$\frac{(x+5)-(x-3)}{(x-3)(x+5)}=\frac{1}{6}$Simplifying the numerator and denominator:$\frac{x+5-x+3}{x^{2}+5x-3x-15}=\frac{1}{6}$$\frac{8}{x^{2}+2x-15}=\frac{1}{6}$Cross-multiplying:$x^{2}+2x-15 = 48$$x^{2}+2x-15-48 = 0$$x^{2}+2x-63 = 0$Factoring the quadratic equation:$x^{2}+9x-7x-63 = 0$$x(x+9)-7(x+9) = 0$$(x+9)(x-7) = 0$Setting each factor to zero:$x+9 = 0 \implies x = -9$$x-7 = 0 \implies x = 7$Thus,the roots of the equation are $-9$ and $7$.

Solve the following equation using the method of factorization: $\frac{1}{x-3}-\frac{1}{x+5}=\frac{1}{6} \,(x \neq 3, -5)$

Similar Questions

The length of a rectangular garden exceeds its breadth by $6 \, m$. If the area of the garden is $216 \, m^2$,find the length and the breadth of the garden.

Solve the following equation using the method of factorization and write its solution set: $\frac{8}{x+5} = \frac{3}{x-1} + \frac{1}{x-5}$

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?

The sum of a natural number and its reciprocal is $\frac{5}{2}$. Then the number is $\ldots \ldots .$

Find the roots of the following quadratic equation by factorisation:
$100 x^{2}-20 x+1=0$

Vedclass Test Series

Exam Paper Generator

Online Exam Module