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AlekseyPX
3 years ago
9

Find the lowest common denominator of p+3/p2+7p+10 and p5/p2+5p+6

Mathematics
2 answers:
NeTakaya3 years ago
6 0

Answer:  The required lowest common denominator of both the fractions is x^3+10x^2+31x+30.

Step-by-step explanation:  We are given to find the lowest common denominator of the following two fractions :

f_1=\dfrac{p+3}{p^2+7p+10},~~~f_2=\dfrac{p+5}{p^2+5p+6}.

After factorizing the denominators, the fractions become

f_1=\dfrac{p+3}{p^2+7p+10}=\dfrac{p+3}{p^2+5p+2p+10}=\dfrac{p+3}{(p+2)(p+5)},\\\\\\f_2=\dfrac{p+5}{p^2+5p+6}=\dfrac{p+5}{p^2+3p+2p+6}=\dfrac{p+5}{(p+2)(p+3)}.

Therefore, the lowest common denominator of both the fractions is

L.C.M.((x+2)(x+5),(x+2)(x+3))\\\\=(x+2)(x+3)(x+5)\\\\=(x^2+5x+6)(x+5)\\\\=x^3+5x^2+6x+5x^2+25x+30\\\\=x^3+10x^2+31x+30.

Thus, the required lowest common denominator of both the fractions is x^3+10x^2+31x+30.

Sunny_sXe [5.5K]3 years ago
4 0
(P+1)(p+2)(p+5) is LCM
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