How do you subtract #1/(x-6) - 3/(x+6) + (3x)/(36-x^2)#?

Answer 1

#1/(x-6)-3/(x+6)+(3x)/(36-x^2)=(24-5x)/(x^2-36)#

#1/(x-6)-3/(x+6)+(3x)/(36-x^2)#
= #1/(x-6)-3/(x+6)-(3x)/(x^2-36)#
As GCD of #(x-6)#, #(x+6)# and #(x^2-36)# is #(x^2-36)=(x-6)(x+6)#, above can be written as
#((x+6)-3(x-6)-3x)/(x^2-36)#
= #(x+6-3x+18-3x)/(x^2-36)#
= #(24-5x)/(x^2-36)#
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Answer 2

To subtract the given expressions, we need to find a common denominator. The common denominator for the three fractions is (x-6)(x+6)(6-x^2).

Next, we multiply each fraction by the appropriate factors to obtain the common denominator.

For the first fraction, we multiply the numerator and denominator by (x+6)(6-x^2). For the second fraction, we multiply the numerator and denominator by (x-6)(6-x^2). For the third fraction, we multiply the numerator and denominator by (x-6)(x+6).

After multiplying, we simplify the numerators and combine like terms.

The resulting expression is:

[(x+6)(6-x^2) - 3(x-6)(6-x^2) + 3x(x-6)(x+6)] / [(x-6)(x+6)(6-x^2)]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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