Find the LCD of the following expressions. Write LCD in factored form. 516p2+8p+1 and 4p−8p2+10p+3 LCD: ?

Step by step solution to "Find the LCD of the following expressions. Write..."

sanuluy

Answered question

2021-10-13

Find the LCD of the following expressions. Write LCD in factored form.

\frac{5}{16 p^{2} + 8 p + 1}

and

\frac{4 p}{- 8 p^{2} + 10 p + 3}

LCD: ?

Answer & Explanation

unett

Skilled2021-10-14Added 119 answers

Step 1
To determine:
LCD for the given expression:
Solution:
Least Common Denominator is the lowest common multiple of the denominators of a set of fractions;
Step 2
Considering
We have:

16 p^{2} + 8 p + 1

= 16 p^{2} + (4 + 4) p + 1

= 16 p^{2} + 4 p + 4 p + 1

= 4 p (4 p + 1) + (4 p + 1)

= (4 p + 1) (4 p + 1)

Consider the another denominator:

- 8 p^{2} + 10 p + 3

= - 8 p^{2} + (12 - 2) p + 3

= - 8 p^{2} + 12 p - 2 p + 3

= - 4 p (- 2 p + 3) + (- 2 p + 3)

= (4 p + 1) (- 2 p + 3)

Step 3 Hence,
least common multiple for both the denominators is:

(4 p + 1) (- 2 p + 3)

Hence,
The LCD for both the expressions is:

(4 p + 1) (- 2 p + 3)

\frac{5}{16 p^{2} + 8 p + 1}

and

\frac{4 p}{- 8 p^{2} + 10 p + 3}

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