1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
seraphim [82]
3 years ago
9

Please show your work and explain it.

Mathematics
1 answer:
Maru [420]3 years ago
6 0

Answer:

f(x)=\dfrac{x+2}{2(x-2)}

Step-by-step explanation:

Remember when you divide fractions, you need to get the reciprocal of the divisor and multiply. So your first simplification would be:

\dfrac{x^2+4x+4}{x^2-6x+8}\div\dfrac{6x+12}{3x-12}\\\\=\dfrac{x^2+4x+4}{x^2-6x+8}\times\dfrac{3x-12}{6x+12}\\\\=\dfrac{(x^2+4x+4)(3x-12)}{(x^2-6x+8)(6x+12)}

Next we factor what we can so we can further simplify the rest of the equation:

=\dfrac{(x^2+4x+4)(3x-12)}{(x^2-6x+8)(6x+12)}\\\\=\dfrac{(x+2)(x+2)(3x-12)}{(x^2-6x+8)(6(x+2))}\\\\

We can now cancel out (x+2)

=\dfrac{(x+2)(3x-12)}{(x^2-6x+8)(6)}

Next we factor out even more:

=\dfrac{(x+2)(3)(x-4)}{(x-2)(x-4)(6)}

We cancel out x-4 and reduce the 3 and 6 into simpler terms:

=\dfrac{(x+2)(1)}{(x-2)(2)}

And we can now simplify it to:

=\dfrac{x+2}{2(x-2)}

You might be interested in
The expression 0.08 + (x-200) models the final price of a computer with an instant rebate in a state that charges a sales tax.
Kobotan [32]
It looks like the answer is D
7 0
2 years ago
Suppose S and T are mutually exclusive events. Find P(S or T)? sp(S) = 6/11 and p(t)= 1/10
Sholpan [36]
Using P(A∪B) = P(A) + P (B) - P(A∩B) 
If we apply this in the question 
Then P(S∪T) = P(S) + P(T) - P (S∩T)
                      = 6/11 + 1/10 - P (S∩T)
                      = 71/110 - P (S∩T)
But events S and T are mutually exclusive events therefore, 
P(S∩T) = 0,
Hence P(S∪T) = 71/110
3 0
2 years ago
(Geometry) Suppose the amount of water in the container is exactly enough to fill the cone. The container is held so that the he
Lesechka [4]

Answer:

killfuyy

Step-by-step explanation:

told you to shoot yourself

7 0
2 years ago
what is the sum of the measures of the angles of a convex quadrilateral? will this property hold if the quadrilateral is not con
bonufazy [111]

Answer:

The sum of the measures of the angles of a convex quadrilateral is 360° as a convex quadrilateral is made of two triangles. Yes, this property also holds true for a quadrilateral which is not convex. This is because any quadrilateral can be divided into two triangles.

3 0
2 years ago
Find the equation of the straight line joining the points (-5,2) and (3,-4)​
Anastaziya [24]

Answer:

3x+4y+7=0.... equations (1)

which is required equations

6 0
3 years ago
Read 2 more answers
Other questions:
  • X take away 7 is greater than 10
    10·1 answer
  • I need help with number 6
    12·2 answers
  • 3= n/5 find value of n
    13·2 answers
  • Bridget has swimming lessons every fifth day and diving lessons every third day. If she had a swimming lesson and a diving lesso
    11·1 answer
  • (no links please) For each inequality, decide whether the solution is represented by
    9·1 answer
  • ANSWER FAST PLEASE PLEASE PLEASE
    10·2 answers
  • A car dealership sold 36 cars in April. The dealership wants to increase the number of cars sold by 40% in May. How many cars wi
    15·1 answer
  • Algebra help please answer
    8·1 answer
  • HELP!!
    12·1 answer
  • A commercial greenhouse is constructed
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!