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3 years ago

6

What is the simplified form of x plus 1 over x squared plus x minus 6 divided by x squared plus 5x plus 4 over x plus 3 ?

2 answers:

kirill115 [55]3 years ago

6 0

X² + x - 6 = x² + 3 x - 2 x - 6 = x ( x + 3 ) - 2 ( x + 3 ) = ( x + 3 ) ( x - 2 )
x² + 5 x + 4 = x² + x + 4 x + 4 = x ( x + 1 ) + 4 ( x + 1 ) = ( x + 1 ) ( x + 4 )
( x + 1 ) / ( x² + x - 6 ) : ( x² + 5 x + 4 ) / ( x + 3 ) =
= ( x + 1 ) / ( x² + x + 6 ) · ( x + 3 ) / ( x² + 5 x + 4 ) =
= ( x + 1 ) / ( x + 3 ) ( x - 2 ) · ( x + 3 ) / ( x + 1 ) ( x + 4 ) =
= 1 / ( x - 2)( x + 4 )

Jobisdone [24]3 years ago

3 0

Answer:

1 / (x + 3) (x - 2)

Step-by-step explanation:

This is the correct answer i just took the test!

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3 years ago

Read 2 more answers

In answering on a multiple choice test, a student either know the answer or guesses. Let p be the probability that the students

LenaWriter [7]

Answer:

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Step-by-step explanation:

For mutually exclusive events as A1, A2, A3, etc, Bayes' theorem states:

$P(A|B)= \frac{P(B|A)P(A)}{P(B)}$

P(A|B) is a conditional probability: the likelihood of event A occurring given that B is true.

P(B|A) is a conditional probability: the likelihood of event B occurring given that A is true.

P(A) is the probability that A occurs

P(B) is the probability that B occurs

For this problem:

A1 is the probability that the student knows the answer

A2 is the probability that the student guesses the answer

B is the probability that the student answer correctly

$P(A_{1})=p \\P(A_{2})=1-p \\P(B|A_{1})=1 \\P(B|A_{2})=\frac{1}{m} \\P(B)= P(A_{1})P(B|A_{1}) + P(A_{2})P(B|A_{2})= p+\frac{1-p}{m} \\$

P(B|A₁) means the probability that the answer is correct when he knew the answer

P(B|A₂) means the probability that the answer is correct when he guessed the answer

P(A₁|B) means the probability that he knew the answer when the answer was correct

Replacing everything in the Bayes' theorem you get:

$P(A_{1}|B)= \frac{P(B|A_{1})P(A_{1})}{P(B)}=\frac{(1)(p)}{p+\frac{1-p}{m}} =\frac{mp}{mp+1-p} =\frac{mp}{1+p(m-1)}$

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