Math Question, Algebra 2?

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p + 8/p= -9 Multiplying both sides by p,we get
p^2+8= -9p
p^2+9p+8=0
(p+1)(p+8)=0
p= -1 or -8

**** be conscious: because you've different that aces do count number as being less than 9, I genuinely have gotten rid of all my references to the prospect that Aces do not count number.***** threat is expressed as a fragment "favorable/possible." for each situation, "possible" is the style of recommendations of drawing 2 playing cards out of fifty 2 (which one we draw first would not count number). We call that fifty 2-elect-2, and that is equivalent to (fifty 2! / (2! *(fifty 2-2)!)) that is equivalent to fifty 2*fifty one / 2, or, 1326 So there are 1326 possible recommendations to entice 2 playing cards. What about favorable? properly, considering the fact that there are 13 hearts, the style of recommendations to entice 2 hearts is 13-elect-2. that is equivalent to (13! / (2! *(13-2)!)) or, seventy 8. for this reason, the threat of drawing 2 hearts is seventy 8 / 1326, or 39/663, that is about a 6% possibility. for 2 numbers below 9, we opt to recognize what number there are interior the deck. If Aces count number (as "a million"), then there are 32 such playing cards. So the favorable consequences are 32-elect-2. (32! / (2! *(32-2)!)) = 496 So the threat is 496/1326 = 248/663. that is about a 37% possibility. playstation fifty 2! is fifty 2 factorial and it skill fifty 2 * fifty one * 50......* 2 * a million **** Ah, so do you want to understand the prospect of having both of those consequences? Many have instructed you to operate both possibilities at the same time. yet to attain this can be to ignore the actual undeniable reality that many of the suited consequences are both 2 hearts AND 2 numbers below 9! what number consequences overlap? properly, there are 8 hearts less than 9. So the recommendations to entice 2 of them are 8-elect-2. that is (8! / (2! *(8-2)!)), or 28. to locate the threat of both outcome, we count number favorable consequences like this: style of recommendations to entice 2 hearts PLUS recommendations to entice 2 numbers below 9 MINUS style of recommendations that overlap. So: seventy 8 + 496 - 28, or 546 favorable consequences. The threat is 546/1326, or ninety one/221, that is about a 40-one% possibility, no longer 40 3%.

p² + 8 = - 9p
p² + 9p + 8 = 0
(p + 1)(p + 8) = 0
p = - 1 , p = - 8

p + (8/p) = -9
p[p + (8/p)] = p(-9)
p^2 + 8 = -9p
p^2 + 8 + 9p = 0
p^2 + 9p + 8 = 0
(p + 1)(p + 8) = 0 (factorize)

p + 1 = 0
p = -1

p + 8 = 0
p = -8

∴ p = -1 or -8

(p² + 8)/p = -9
p² + 8 = -9p
p² + 9p + 8 = 0
(p + 8)(p + 1) = 0

p = -8 or p = -1

multiply throughout by p

p * p + (8/p)*p = -9 * p
p^2 + 8 = -9p
p^2 + 9p + 8 = 0
Now factorise:
(p+1) (p+8) = 0
p = -1, -8.

p + (8/p) = -9; multiply everything through by p

p^2 + 8 = - 9p; which becomes

p^2 + 9p +8 = 0; which factors to

(p + 8) (p + 1) = 0; implying p = -8 or p = -1

Make the LHS into a single fraction:

(p² + 8)/p = -9
p² + 8 = -9p
p² + 9p + 8 = 0
(p + 8)(p + 1) = 0

So p = -8 or p = -1

p=-1

Multiply everything by p.

p^2 + 8 = -9p.
p^2 + 9p + 8 = 0.
(p + 8)(p + 1) = 0.
p = -8.
p = -1.

Upon inspection, p = -1 isn't a solution when you plug it back into the solution.

Answer: p = -8.