For what value of will \(\frac{3+x}{5+x}\) and \(\frac{1+x}{2+x} \)be equal?

Creampuff Aug 23, 2020

#1**+2 **

1. Put it into an equation (3+x)/(5+x)=(1+x)/(2+x).

2. Cross mulitply, (1+x)*(5+x)=(3+x)*(2+x)

Try taking it from there. I figured that giving the answer is probably not very effective. You can ask questions if you still don't understand.

joliel3 Aug 23, 2020

#2**0 **

hmm i am so sorry could you do a step by step including how you got the answer because my mom also wants to know thanks in advance :D

Creampuff Aug 23, 2020

#4**+1 **

Sure!

1. So let's simplify (1+x)*(5+x)=(3+x)*(2+x) using the First Outer Inner Last method.

2. (1+x)*(5+x)...

First: 1*5=5

Outer: 1*x=x

Inner: x*5=5x

Last: x*x=x^2

Sum: 5+x+5x+x^2=6x+5+x^2

3. (3+x)*(2+x)...

First: 3*2=6

Outer: 3*x=3x

Inner: x*2=2x

Last: x*x=x^2

Sum: 6+3x+2x+x^2=5x+6+x^2

4. Rewrite equation as 6x+5+x^2=5x+6+x^2

5. Subtract 5 from both sides turning the equation into 6x+x^2=5x+1+x^2

6. Cancel out x^2 from both sides turning the equation into 6x=5x+1.

7. Subtract 5x from both sides and you get x=1.

**Answer: x=1 **

joliel3 Aug 23, 2020