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Algebra and Applications Test 2

Question : 14 of 40

Marks: +1, -0

\frac{1}{x-3} - \frac{1}{x+5} = \frac{1}{6}

are:

Solution: 👈: Video Solution

Concept:

Solving a rational equation by combining fractions, cross-multiplying, and factoring the resulting quadratic.

Explanation:

Given:

\frac{1}{x-3} - \frac{1}{x+5} = \frac{1}{6}

Note:

x \neq 3

and

x \neq -5

Combine the left side:

\frac{(x+5)-(x-3)}{(x-3)(x+5)} = \frac{8}{(x-3)(x+5)}

So,

\frac{8}{(x-3)(x+5)} = \frac{1}{6}

Cross-multiply:

48 = (x-3)(x+5)

48 = x^2+2x-15

Rearrange:

x^2+2x-63=0

Split the middle term:

x^2+9x-7x-63=0

x(x+9)-7(x+9)=0

(x+9)(x-7)=0

Thus,

x=-9

x=7

Both values are valid since they are not

3

-5

Answer:

x=7, -9

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