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
mamaluj [8]
4 years ago
9

Solving Rational equations. LCD method. Show work. Image attached.

Mathematics
1 answer:
posledela4 years ago
4 0

(k-2)(k-6)=k^2-2k-6k+12=k^2-8k+12

So in order to get all the fractions to have a common denominator, we need to multiply \dfrac k{k-2} by \dfrac{k-6}{k-6}, and \dfrac1{k-6} by \dfrac{k-2}{k-2}:

\dfrac k{k-2}\cdot\dfrac{k-6}{k-6}=\dfrac{k(k-6)}{(k-2)(k-6)}=\dfrac{k^2-6k}{k^2-8k+12}

\dfrac1{k-6}\cdot\dfrac{k-2}{k-2}=\dfrac{k-2}{(k-2)(k-6)}=\dfrac{k-2}{k^2-8k+12}

Now,

\dfrac4{k^2-8k+12}=\dfrac{(k^2-6k)+(k-2)}{k^2-8k+12}

As long as k\neq2 and k\neq6 (which we can't have because otherwise k^2-8k+12=0), we can cancel k^2-8k+12 in the denominators on both sides:

4=(k^2-6k)+(k-2)

4=k^2-5k-2

0=k^2-5k-6

We can factorize the right side:

0=(k-6)(k+1)

which tells us that k=6 and k=-1 are solutions.

You might be interested in
Please help this is very important
shusha [124]

Answer:

Answer is D pls mark me as a brainlist

7 0
3 years ago
What time is it 2 hours and 50 minutes before 9:30 A.M.?
AnnyKZ [126]

9:30 am

go back 3 hours

6:30 am

add 10 minutes

6:40 am

8 0
3 years ago
Y<br> =<br> x<br> −<br> 4<br> y=x−4<br> 3<br> x<br> +<br> y<br> =<br> −<br> 8<br> 3x+y=−8
Lemur [1.5K]

Answer:

what is your question?

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Please help me and explain if you can
SOVA2 [1]

Answer:

maybe Neither ( I really don't know the answer )

3 0
3 years ago
Jack and his children went into a restaurant where they sell hamburgers for $6 each and tacos for $2 each. Jack has $30 to spend
irina [24]
128..........................................
4 0
3 years ago
Read 2 more answers
Other questions:
  • (2,4) (x,8) slope = -2
    13·1 answer
  • If isosceles triangle ABC has a 130° angle at vertex B, which statement must be true?
    8·2 answers
  • If you graph 2y+8=6x^2-10x what will be the y intercept?
    8·1 answer
  • A jigsaw puzzle has 289 pieces. each piece is basically a square. how can it be arranged so that
    15·1 answer
  • The area A of a rectangular garden is given by the expression2^2+ 2 − 12. The length L of the garden is
    11·1 answer
  • How I can round it I need help with
    8·2 answers
  • Need help will give you the brainliest
    10·1 answer
  • Which of the following must be true? The diagram is not to scale​
    11·1 answer
  • This system of equations has been placed in a matrix:
    14·1 answer
  • Coats are highly seasonal items. Their highest selling month is 450% of their lowest selling month. During the lowest selling mo
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!