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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Answer: The correct option are as follows;

(1) The triangles are similar because corresponding sides are congruent

(2) The triangles are similar because alternate interior angles are congruent

(3) In the similar triangles, Angle 3 and Angle 6 are corresponding angles

Step-by-step explanation: Please refer to the picture attached for details.

The line i and line e has been drawn and marked as parallel lines. Also two transversal lines m and n have been drawn to intersect in the region between the parallel lines to form two triangles (as shown in the picture).

From the information given, where line e intersects with line n we have angle 1, and where line e intersects with line m we have angle 3, and then the third angle is angle 2.

Furthermore, where line l intersects line m we have angle 6, and where line l intersects line n is angle 4. Also in this second triangle, the third angle is 5.

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