What multiplies to 24 and adds to 20

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

4 years ago

a store selling a couch for $623 on a 24 month payment plan if your down payment of 152 is given and no interest is charged how

sveticcg [70]

First start with $623 and subtract the $152 deposit. Then divide that answer by 24, which equals 19.625. The monthly payment would be 19.63 monthly for 24 months.

3 0

3 years ago

Read 2 more answers

Evaluate the function f(x)=x^2+6x+2 at the given values of the independent variable and simplify.

____ [38]

Answer:

a) 18

b)x^2+10x+18

c)x^2 -6x+2

Step-by-step explanation:

This is a case of plugging in the value into f(x).

a) f(-8)= -8^2 + 6(-8) +2

f(-8)= 64 + (-48) +2

f(-8)=64 + (-46)

f(-8)=18

b) f(x+2)= (x+2)^2+6(x+2)+2

So here I'll take a break to explain what's going on, because x+2 is a binomial meaning two terms and it is being squared I have to multiply the whole thing by itself. Meaning: (x+2) x (x+2), this is also known as foiling!! and for the next part its distributing 6 into x and 2.

f(x+2)= x^2+4x+4+6x+12+2

I'll reorder it

f(x+2)= x^2+4x+6x+12+2+4

f(x+2)= x^2+10x+18

c) f(-x)= -x^2+6(-x) +2

f(-x)= x^2 -6x+2

6 0

3 years ago

I just need yall help ... {:

KonstantinChe [14]

Answer:C

Step-by-step explanation:

The answer is C because the minimum is 33 and the maximum is 51. The first quartile is 33. THE SECOND QUATILE IS 39 and the 3rd quartile is 47.

4 0

3 years ago

Read 2 more answers

If the graph of the following parabola is shifted two units left and three units down, what is the resulting equation?

mafiozo [28]

Answer:

$x=-8\left(y+3\right)^2-2$

Step-by-step explanation:

Because the x and y have been reversed in this equation, shifting the parabola to the left will be outside of the exponent and shifting up and down will be inside with the exponent.

The equation becomes $x=-8\left(y+3\right)^2-2$ .

Where subtracting by 2 moves it two units to the left and adding by 3 moves it 3 units down.

7 0

3 years ago