How do you combine #m/(20+9m+m^2)-4/(12+7m+m^2)#?

Answer 1

Eli Assouline

#((m-5))/((5+m)(3+m))#

Factorise the denominators first.

#m/(20+9m+m^2)-4/(12+7m+m^2)#

=#m/((5+m)(4+m))-4/((3+m)(4+m))#

#"Find a common denominator"#

=#(m(3+m) - 4(5+m))/((5+m)(4+m)(3+m))#

=#(3m +m^2 -20-4m)/((5+m)(4+m)(3+m))#

=#(m^2 -m-20)/((5+m)(4+m)(3+m))#

=#((m-5)(m+4))/((5+m)(4+m)(3+m))#

#((m-5)cancel((m+4)))/((5+m)cancel((4+m))(3+m))#

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Answer 2

Eva Adamson

To combine the given expressions, you need to find a common denominator and then simplify the resulting expression. The common denominator for the two fractions is (m^2 + 9m + 20)(m^2 + 7m + 12). After finding the common denominator, you can combine the fractions by subtracting the numerators and placing the result over the common denominator. Finally, simplify the expression if possible.

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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.