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3 years ago

Solve for all values of p:

Mathematics

1 answer:

Alchen [17]3 years ago

3 0

Answer:

p = - 5, p = - 1

Step-by-step explanation:

Given

$\frac{3p}{p-5}$ - $\frac{2}{p+3}$ = $\frac{p}{p+3}$

Multiply through by the LCM of (p - 5)(p + 3)

3p(p + 3) - 2(p - 5) = p(p - 5) ← distribute parenthesis

3p² + 9p - 2p + 10 = p² - 5p

3p² + 7p + 10 = p² - 5p ( subtract p² - 5p from both sides )

2p² + 12p + 10 = 0 ← divide through by 2

p² + 6p + 5 = 0 ← in standard form

(p + 1)(p + 5) = 0 ← in factored form

Equate each factor to zero and solve for p

p + 1 = 0 ⇒ p = - 1

p + 5 = 0 ⇒ p = - 5

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