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Find the LCD of the given rational equation

Find the LCD of the given rational equation-example-1
User Numentar
by
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1 Answer

4 votes

Answer:


=(2x^3+x^2-11x+14)/(\left(x+4\right)\left(x+2\right)\left(x-2\right))

Explanation:

Step 1: Factor
x² + 2x - 8: (x - 2) (x + 4)


=(x)/(x+4)+(x-1)/(x+2)+(3)/(\left(x-2\right)\left(x+4\right))

Step 2: Find the Least Common Multiplier of
x + 4, x - 2, (x + 4), (x - 2)

=
(x + 4) (x + 2) (x - 2)

Step 3a: Conform the fractions based on the LCM (Least Common Multiplier)

=
(x\left(x+2\right)\left(x-2\right))/(\left(x+4\right)\left(x+2\right)\left(x-2\right))+(\left(x-1\right)\left(x+4\right)\left(x-2\right))/(\left(x+2\right)\left(x+4\right)\left(x-2\right))+(3\left(x+2\right))/(\left(x-2\right)\left(x+4\right)\left(x+2\right))

Step 3b: The denominators are equal, so combine the fractions.


=(x\left(x+2\right)\left(x-2\right)+\left(x-1\right)\left(x+4\right)\left(x-2\right)+3\left(x+2\right))/(\left(x+4\right)\left(x+2\right)\left(x-2\right))

Step 4: Expand
x(x + 2)(x - 2) +(x-1)(x+4)(x-2) + 3(x-2)


=(2x^3+x^2-11x+14)/(\left(x+4\right)\left(x+2\right)\left(x-2\right))

Have a great day!

User Rehan Ch
by
7.2k points