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How do you combine #2/(3x-15)+x/(25-x^2)#?

Answer 1

Nathan Axel

#2/(3x-15)+x/(25-x^2)=(10-x)/(3x^2-75)#

#2/(3x-15)+x/(25-x^2)#

= #2/(3(x-5))-x/(x^2-25)# - we have modified so that both may have common factor #(x-5)#

= #2/(3(x-5))-x/(x^2-5^2)#

= #2/(3(x-5))-x/((x-5)(x+5))#

= #(2(x+5)-3x)/(3(x-5)(x+5))#

= #(2x+10-3x)/(3(x-5)(x+5))#

= #(10-x)/(3(x-5)(x+5))#

= #(10-x)/(3(x^2-25))#

= #(10-x)/(3x^2-75)#

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Answer 2

Eva Abramson

To combine the expressions 2/(3x-15) and x/(25-x^2), we need to find a common denominator. The common denominator for these two expressions is (3x-15)(25-x^2).

Next, we multiply the first fraction, 2/(3x-15), by (25-x^2)/(25-x^2), and the second fraction, x/(25-x^2), by (3x-15)/(3x-15).

After multiplying and simplifying, we can combine the numerators over the common denominator.

The resulting expression is (2(25-x^2) + x(3x-15))/(common denominator).

Simplifying further, we get (50 - 2x^2 + 3x^2 - 15x)/(common denominator).

Combining like terms in the numerator, we have (x^2 - 15x + 50)/(common denominator).

Therefore, the combined expression is (x^2 - 15x + 50)/(3x-15)(25-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.