Question

Classify the solutions of 3 over x plus 5, plus one fifth, equals 2 over x plus 5 as extraneous or non-extraneous.

Answer 1

@Algorithmic @ganeshie8 @CaptainLlama49

Answer 2

is the answer extraneous?

Answer 3

I have typed this twice and lost it both times. I will try one more time.

Answer 4

ok:)

Answer 5

\[\frac{3}{x+5}+\frac{1}{5}=\frac{2}{x+5}\]

Answer 6

Common denominator is 5(x+5).
Multiply each term by that.

Answer 7

so you get 15/5(x+5)+x+5/5(x+5)=10/5(x+5)

Answer 8

\[5(x+5)(\frac{3}{x+5})+5(x+5)(\frac{1}{5})=5(x+5)(\frac{3}{x+5})\]

Answer 9

Cancel all the denominators.

Answer 10

\[15 +x+5=10\]

Answer 11

yup! :)

Answer 12

The 3 on the right side is supposed to be a 2

Answer 13

\[x=-10\]

Answer 14

Now. Is that extraneous or not? Does it cause any denominator to be 0? Does it make the original equation true?

Answer 15

extraneous?

Answer 16

Why is it extraneous?

Answer 17

3/ -5 +1/5 = 2/-5

Answer 18

I don't know. When i plugged it in, that's the equation I got above,

Answer 19

\[-\frac{3}{5}+\frac{1}{5}=-\frac{2}{5}\]

Answer 20

Is that true or not?

Answer 21

Is any denominator equal to 0 ?

Answer 22

no

Answer 23

Then it is a perfectly fine solution and is not extraneous.

Answer 24

Oh!

Answer 25

Thank you:)

Answer 26

Can I ask one more?

Answer 27

An extraneous solution is a number that appears to be a solution but doesn't hold up to scrutiny because it either doesn't check or causes a denominator to be 0.

Answer 28

Yes

Answer 29

Solve for x: 2 over 5 plus 3 over 5 x equals quantity x plus 5 over 10.

Answer 30

Okay! I understand now:)

Answer 31

For this one, I got x=-3,2

Answer 32

\[\frac{2}{5}+\frac{3}{5x}=\frac{x+5}{10}\]

Answer 33

Is that it?

Answer 34

yeah:)

Answer 35

\[10x(\frac{2}{5})+10x(\frac{3}{5x})=10x(\frac{x+5}{10})\]

Answer 36

\[4x+6=x^2+5x\]

Answer 37

-1x^2+5x+36

Answer 38

\[x^2+x-6=0\]

Answer 39

\[(x+3)(x-2)=0\]

Answer 40

So, -3 and 2 ?

Answer 41

\[x=-3,2\]

Answer 42

Last one:)?

Answer 43

\[\frac{2}{5}+\frac{3}{5(-3)}=\frac{-3+5}{10}\]

Answer 44

\[\frac{2}{5}-\frac{3}{15}=\frac{2}{10}\]

Answer 45

\[\frac{2}{5}-\frac{1}{5}=\frac{1}{5}\]

Answer 46

That seems to check. Try 2. See if it checks.

Answer 47

Okay, that makes sense!! :D

Answer 48

Classify the solutions of 1 over x plus 4, plus one half, equals 1 over x plus 4 as extraneous or non-extraneous.

Answer 49

So, I got -4

Answer 50

\[\frac{1}{x+4}+\frac{1}{2}=\frac{1}{x+4}\]

Answer 51

And -4 causes the denominator to be 0 so it is extraneous.

Answer 52

yes, I agree

Answer 53

Good job!!

Answer 54

Solve for x: 1 over 2 plus 4 over 2 x equals quantity x plus 4 over 10.

Answer 55

Me too. Did you check them?

Answer 56

They both check.