2(w + 2w+6) = 9090
6w + 12 = 9090
6w = 9078
w = 1513m
l = 2w+6 = 3032m
“Extraneous solutions are not solutions at all. They arise from outside the problem, from the method of solution. They are extraneous because they are not solutions of the original problem. ... To tell if a "solution" is extraneous you need to go back to the original problem and check to see if it is actually a solution.”
Basically, they are an answer you get when you solve a problem, but they don’t actually make the equation true so you disregard it.
<h2>
Hello!</h2>
The answer is:
![\frac{z-y}{a+b}](https://tex.z-dn.net/?f=%5Cfrac%7Bz-y%7D%7Ba%2Bb%7D)
<h2>
Why?</h2>
We need to simplify the fractions in order to find the answer.
Also, we must remember that:
![a^{2}-b^{2}=(a+b)(a-b)](https://tex.z-dn.net/?f=a%5E%7B2%7D-b%5E%7B2%7D%3D%28a%2Bb%29%28a-b%29)
So, simplificating the first fraction, we have:
![\frac{z^{2} -y^{2}}{a^{2}-b^{2}}=\frac{(z+y)(z-y)}{(a+b)(a-b)}](https://tex.z-dn.net/?f=%5Cfrac%7Bz%5E%7B2%7D%20-y%5E%7B2%7D%7D%7Ba%5E%7B2%7D-b%5E%7B2%7D%7D%3D%5Cfrac%7B%28z%2By%29%28z-y%29%7D%7B%28a%2Bb%29%28a-b%29%7D)
Then, let's divide each fraction:
To divide fractions, we need to multiply the first equation (numerator) by the reciprocal of the the second fraction (denominator).
The reciprocal of the second fraction, for this case, the denominator, is:
![\frac{a-b}{z+y}](https://tex.z-dn.net/?f=%5Cfrac%7Ba-b%7D%7Bz%2By%7D)
Hence,
![\frac{(z+y)(z-y)}{(a+b)(a-b)}*\frac{a-b}{z+y}=\frac{z-y}{a+b}](https://tex.z-dn.net/?f=%5Cfrac%7B%28z%2By%29%28z-y%29%7D%7B%28a%2Bb%29%28a-b%29%7D%2A%5Cfrac%7Ba-b%7D%7Bz%2By%7D%3D%5Cfrac%7Bz-y%7D%7Ba%2Bb%7D)
So, the final fraction is:
![\frac{z-y}{a+b}](https://tex.z-dn.net/?f=%5Cfrac%7Bz-y%7D%7Ba%2Bb%7D)
Have a nice day!
114. This would make 112 the smaller one
114
+112
-------
226