PLEASE HELP!<br> What is the value of x?<br><br><br><br> Enter your answer in the box.<br><br> x =

Which statement best reflects the solution(s) of the equation?

Inessa [10]

x=2 is only solution while x=1 is extraneous solution

Option C is correct.

Step-by-step explanation:

We need to solve the equation $\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}$ and find values of x.

Solving:

Find the LCM of denominators x-1,x and x-1. The LCM is x(x-1)

Multiply the entire equation with x(x-1)

$\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}\\\frac{1}{x-1}*x(x-1)+\frac{2}{x}*x(x-1)=\frac{x}{x-1}*x(x-1)\\Cancelling\,\,out\,\,the\,\,same\,\,terms:\\x+2(x-1)=x^2\\x+2x-2=x^2\\3x-2=x^2\\x^2-3x+2=0$

Now, factoring the term:

$x^2-2x-x+2=0\\x(x-2)-1(x-2)=0\\(x-1)(x-2)=0\\x-1=0\,\,and\,\, x-2=0\\x=1\,\,and\,\, x=2$

The values of x are x=1 and x=2

Checking for extraneous roots:

Extraneous roots: The root that is the solution of the equation but when we put it in the equation the answer turns out not to be right.

If we put x=1 in the equation, $\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}$ the denominator becomes zero i.e

$\frac{1}{1-1}+\frac{2}{1}=\frac{1}{1-1}\\\frac{1}{0}+2=\frac{1}{0}$

which is not correct as in fraction anything divided by zero is undefined. So, x=1 is an extraneous solution.

If we put x=2 in the equation,

$\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}$

$\frac{1}{2-1}+\frac{2}{2}=\frac{2}{2-1}\\\frac{1}{1}+1=\frac{2}{1}\\1+1=2\\2=2$

So, x=2 is only solution while x=1 is extraneous solution

Option C is correct.

Keywords: Solving Equations and checking extraneous solution

Learn more about Solving Equations and checking extraneous solution at:

#learnwithBrainly

5 0

3 years ago

A recipe calls for 3 times as many chocolate chips as butterscotch chips. If there are 25 oz of chocolate chips, how many oz do

Bingel [31]

The amount, in oz of butterscotch chips needed by proportional reasoning is; 75oz.

<h3>What is the amount of butterscotch chips needed by proportional reasoning?</h3>

It follows from the task content that the the amount of butterscotch chips needed can be determined by means of the proportion premise declared in which case;

The recipe requires 3 times as many chocolate chips as butterscotch chips.

Hence, when 25oz of chocolate chips is used, the amount of butterscotch needed is 3 times 25 and hence, = 3 × 25 = 75oz.

Read more on proportion;

brainly.com/question/1496357

#SPJ1

4 0

1 year ago

Solve the following inequality algebraically:<br> look at the picture

seraphim [82]

The answer is b -9 < x < 12

8 0

2 years ago

Please answer thoroughly

aleksklad [387]

Answer:

Part A: 2k(2c2+5(2)-8c-20)

Part B: sorry i don't know how to do this part

Step-by-step explanation:

Part A, you divide each number by 2 first so you get a simplified version of each number. Then, you will quickly realize that the varible k is similar in all of the numbers then you remove that and put it with the 2 outside the (). Hope you understood my explination.

7 0

3 years ago

The age of a father is to less than seven times the age of his son in three years the sum oftheir ages will be 52 if the sons pr

vekshin1

Answer:

The correct answer is:

(7s-2)+3+(s+3) = 52, or 8s+4 = 52.

Step-by-step explanation:

Since s is the son's age, "two less than seven times" the son's age would be represented by 7s-2. To represent this in 3 years, we would add 3: (7s-2)+3. In 3 years, the son's age, s, would be represented by s+3. We are told that the sum of these ages will be 52; this gives us (7s-2)+3+(s+3) = 52.

To simplify this, combine like terms. 7s+s = 8s; -2+3+3 = 4. This gives us 8s+4=52.

3 0

2 years ago

PLEASE HELP! What is the value of x? Enter your answer in the box. x =