Question

Which solution to the equation startfraction 3 over a 2 endfraction startfraction 2 over a endfraction = startfraction 4 a minus 4 over a squared minus 4 endfraction is extraneous?

Answer 1

The solution of the rational equation $\frac{3}{a + 2} * \frac{2}{a} = \frac{4 a - 4 }{a^2 - 4}$ is a = 3

How to determine the solution?

The equation is given as:

$\frac{3}{a + 2} * \frac{2}{a} = \frac{4 a - 4 }{a^2 - 4}$

Express a^2 - 4 as  a difference of two squares

$\frac{3}{a + 2} * \frac{2}{a} = \frac{4 a - 4 }{(a + 2)(a - 2)}$

Cancel out the common terms

$\frac{3}{} * \frac{2}{a} = \frac{4 a - 4 }{a - 2}$

Factor out 2 from 4a - 4

$\frac{3}{} * \frac{2}{a} = \frac{2(a - 2) }{a - 2}$

Evaluate the quotient

$\frac{3}{} * \frac{2}{a} = 2$

Divide both sides by 2

$\frac{3}{1} * \frac{1}{a} = 1$

Cross multiply

a = 3

Hence, the solution of the equation $\frac{3}{a + 2} * \frac{2}{a} = \frac{4 a - 4 }{a^2 - 4}$ is 3

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Answer 2

Answer:

the answer for Which solution to the equation StartFraction 3 Over a + 2 EndFraction + StartFraction 2 Over a EndFraction = StartFraction 4 a minus 4 Over a squared minus 4 EndFraction is EXTRANEOUS? is a: a=-2

Step-by-step explanation: