f(x) = 1/(x+7)+15/(x-8). Find all a for which f(a)=f(a+15).
I understand this so far
f(a)=f(a+15)
1/(7+a) + 15/(a-8) = 1/(a+22) + 15/(a+7)
I have multiplied the LCD of (a-8)(a+7)(a+22)by both sides with no luck.
This is a multiple choice question
a.) -161/8
b.) 120/7
c.) 161/7
d.) -17
I have the answer as
Responses
Math problem still stuck - Ryan, Sunday, October 12, 2008 at 4:05pm
Just plug in the values since it's multiple choice.
Math problem still stuck - Shawn, Sunday, October 12, 2008 at 4:12pm
When I plug in the values what am I looking to find?
Math problem still stuck - bobpursley, Sunday, October 12, 2008 at 4:20pm
If you want to plug in, plug in the answer for a to see if both sides are equal.
Math problem still stuck - Ryan, Sunday, October 12, 2008 at 4:21pm
you want 1/(7+a) + 15/(a-8) = 1/(a+22) + 15/(a+7), your second equation, to be true, so you true the four values of a given in the equation and if both sides are equal, you've found it.
Math problem still stuck - Ryan, Sunday, October 12, 2008 at 4:22pm
*try not true
Math problem still stuck - Shawn, Sunday, October 12, 2008 at 4:32pm
So you are saying that it is none of the multiple choice answers of -161/8,
120/7, 161/7, or -17
?
I don't think Ryan said the answers is none. He said try them to see if both sides are equal. I think it was me a couple of threads ago that I told you to go through it once more to see if it works, that I did it in my head and didn't get any of the answers.
I don't know what is the problem here. If you want to plug the given answers in for a, do it. If not, don't.
I get -21 1/16
In other words none of the above.
(a+15)(a+7)
To solve the equation f(a) = f(a+15), you can start by substituting the given expression f(x) = 1/(x+7) + 15/(x-8) into the equation:
1/(a+7) + 15/(a-8) = 1/(a+22) + 15/(a+7)
Next, you can simplify the equation by finding a common denominator and combining the fractions:
Multiply every term by (a+7)(a-8)(a+22) to clear the denominators:
(a+7)(a-8)(a+22) / (a+7) + (a+7)(a-8)(a+22) / (a-8) = (a+7)(a-8)(a+22) / (a+22) + (a+7)(a-8)(a+22) / (a+7)
Cancel out the denominators:
(a-8)(a+22) + (a+7)(a+22) = (a+22)(a+7) + (a-8)(a+22)
Expand and simplify:
(a^2 + 14a - 176) + (a^2 + 29a + 154) = (a^2 + 29a + 154) + (a^2 - 14a - 176)
Combine like terms:
2a^2 + 43a - 22 = 2a^2 + 43a - 22
The equation simplifies to 0 = 0, which means that the equation is true for all values of a. Therefore, there is no specific value of a that satisfies the equation f(a) = f(a+15).
This means that none of the multiple-choice options (-161/8, 120/7, 161/7, or -17) are correct answers because there is no specific value for a that makes f(a) equal to f(a+15).