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What is the Simplifies form of...
- Thread starter nwelter
- Start date
Hello, nwelter!
\(\displaystyle \displaystyle{\text{Multiply by }\frac{m-1}{m-1}\!:\quad\frac{(m-1)\left[\frac{m+n}{m-1} + n\right]} {(m-1)\left[\frac{m+n}{m-1} - 1\right]} \;=\;\frac{(m+n) + n(m-1)}{(m+n) - (m-1)} \;=\;\frac{m+ n + mn - n}{m + n - m + 1} }\)
. . . . . . . . . . \(\displaystyle = \;\frac{mn + m}{n + 1} \;=\;\frac{m(n+1)}{n+1} \;=\; m\)
\(\displaystyle \displaystyle{\text{Simplify: }\;\frac{\frac{m+n}{m-1}+n} {\frac{m+n}{m-1} -1} }\)
\(\displaystyle \displaystyle{\text{Multiply by }\frac{m-1}{m-1}\!:\quad\frac{(m-1)\left[\frac{m+n}{m-1} + n\right]} {(m-1)\left[\frac{m+n}{m-1} - 1\right]} \;=\;\frac{(m+n) + n(m-1)}{(m+n) - (m-1)} \;=\;\frac{m+ n + mn - n}{m + n - m + 1} }\)
. . . . . . . . . . \(\displaystyle = \;\frac{mn + m}{n + 1} \;=\;\frac{m(n+1)}{n+1} \;=\; m\)
BigGlenntheHeavy
Senior Member
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- Mar 8, 2009
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\(\displaystyle f(x) \ = \ \frac{\frac{m+n}{m-1}+n}{\frac{m+n}{m-1}-1} \ = \ \frac{\frac{m+n+mn-n}{m-1}}{\frac{m+n-m+1}{m-1}}\)
\(\displaystyle = \ \frac{m(n+1)}{m-1}*\frac{m-1}{n+1} \ = \ \frac{m(n+1)}{n+1} \ = \ m\)
\(\displaystyle Restrictions: \ m\not= \ 1, \ n\not= \ -1.\)
\(\displaystyle = \ \frac{m(n+1)}{m-1}*\frac{m-1}{n+1} \ = \ \frac{m(n+1)}{n+1} \ = \ m\)
\(\displaystyle Restrictions: \ m\not= \ 1, \ n\not= \ -1.\)