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

Mathematics

2 answers:

NeTakaya2 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]2 years ago

4 0

(P+1)(p+2)(p+5) is LCM

You might be interested in

Someone please help me

Troyanec [42]

Pythagorean theorem is $a^{2} + b^{2} = c^{2}$
and using that sin is opposite/hypotenuse, you can find the third side of the triangle.
$11^{2}+(adjacent)^{2} = 61^{2} \\ 121+ (adjacent)^{2} = 3721 \\ (adjacent)^{2}=3600 \\ adjacent = 60$
now you know adjacent is 60, so cos=60/61

4 0

2 years ago

The average of 5 numbers is 33. If the average of first 2 numbers is 35 and that of last 2 is 31, then find the 3rd number.

-BARSIC- [3]

The answer is c. 33.

3 0

2 years ago

Read 2 more answers

86 is 45% of what number

Alik [6]

Hello there! We are talking about 86 being part of a number, so we are looking for the whole. To find the number we are looking for, we can write and solve a proportion. Set it up like this:

86/x = 45/100

86 is 45% of a number. We know the part, so now we are looking for the whole. 45% is part of 100%, so we put that part together. Cross multiply the digits. 100 * 86 is 8,600. 45 * x is 45x. That simplifies to 8,600 = 45x. Now, divide each side by 45 to isolate the x. 45x/45 cancels out. 8,600/45 is 191.1111111 or 191 1/9 in fraction form. There. x = 191 1/9 86 is 45% or 191 1/9

Note: Or, if you have to round to the nearest whole number, the answer is 191, or if you have to round to the nearest tenth, the answer is 191.1. It all depends on if the answer needs to be rounded or exact.

4 0

2 years ago

What is the value of x in the figure please help I’ll give you brainliest :)

Licemer1 [7]

Answer:

37°

Step-by-step explanation:

(4x + 2)° = 150° [Vertically Opposite Angles]

=> 4x = 150 - 2

=> 4x = 148

$= > x = \frac{148}{4}$