You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an alternative browser.
You should upgrade or use an alternative browser.
Rational Expression: 1+6w/w^2-6w+9=18/w^2-6w+9
- Thread starter nickilin
- Start date
Re: Rational Expression
Yep. Plug it back in to see if both sides are equal!
Left hand side:
\(\displaystyle \frac{1 + 6w}{w^{2} - 6w + 9}\)
\(\displaystyle = \frac{1 + 6\left(\frac{17}{6}\right)}{\left(\frac{17}{6}\right)^{2} - 6\left(\frac{17}{6}\right) + 9}\)
\(\displaystyle = \frac{18}{\frac{289}{36} - 17 \cdot \frac{36}{36} + 9 \cdot \frac{36}{36}}\)
\(\displaystyle = \frac{18}{\frac{289}{36} - \frac{612}{36} + \frac{324}{36}}\)
\(\displaystyle = \frac{18}{\frac{1}{36}}\)
\(\displaystyle = 648\)
Right hand side:
\(\displaystyle \frac{18}{w^{2} - 6w + 9}\)
\(\displaystyle = \frac{18}{\left(\frac{17}{6}\right)^{2} - 6\left(\frac{17}{6}\right) + 9}\)
Denominator is the same as the left hand side ... so ...
\(\displaystyle = \frac{18}{\frac{1}{36}}\)
\(\displaystyle = 648\)
Enough proof for ya? :wink:
Yep. Plug it back in to see if both sides are equal!
Left hand side:
\(\displaystyle \frac{1 + 6w}{w^{2} - 6w + 9}\)
\(\displaystyle = \frac{1 + 6\left(\frac{17}{6}\right)}{\left(\frac{17}{6}\right)^{2} - 6\left(\frac{17}{6}\right) + 9}\)
\(\displaystyle = \frac{18}{\frac{289}{36} - 17 \cdot \frac{36}{36} + 9 \cdot \frac{36}{36}}\)
\(\displaystyle = \frac{18}{\frac{289}{36} - \frac{612}{36} + \frac{324}{36}}\)
\(\displaystyle = \frac{18}{\frac{1}{36}}\)
\(\displaystyle = 648\)
Right hand side:
\(\displaystyle \frac{18}{w^{2} - 6w + 9}\)
\(\displaystyle = \frac{18}{\left(\frac{17}{6}\right)^{2} - 6\left(\frac{17}{6}\right) + 9}\)
Denominator is the same as the left hand side ... so ...
\(\displaystyle = \frac{18}{\frac{1}{36}}\)
\(\displaystyle = 648\)
Enough proof for ya? :wink: