Strategy for Simplfication?

TheJason

Administrator
Staff member
Administrator
Moderator
Jan 25, 2018
2,507
545
113
jasonyankee.info
Simplify

@MarkFL @harpazo this seems like this might go on forever.

\(\displaystyle \dfrac{3}{5b} - \dfrac{2}{4b} + \dfrac{1}{7c} + \dfrac{7}{21c}\)

\(\displaystyle \dfrac{-2}{4b} + \dfrac{1}{7c}\)

\(\displaystyle \dfrac{(-2)(7c) + (4b)(1)}{(4b)(7c)} = \dfrac{(-2)(7c)}{(4b)(7c)} + \dfrac{(4b)(1)}{(4b)(7c)}\)

Cancel out stuff.

\(\displaystyle \dfrac{-2}{4b} + \dfrac{1}{7c}\)

\(\displaystyle \dfrac{3}{5b} -\dfrac{2}{4b} + \dfrac{1}{7c}+ \dfrac{7}{21c}\)
 

MarkFL

La Villa Strangiato
Staff member
Administrator
Moderator
Math Helper
Jan 25, 2018
3,495
4,276
113
St. Augustine
I noticed you were ending up where you started on several threads. I think what is intended here is to combine all terms...

\(\displaystyle \frac{3}{5b}-\frac{2}{4b}+\frac{1}{7c}+\dfrac{7}{21c}=\)

\(\displaystyle \frac{3}{5b}\cdot\frac{3\cdot4\cdot7c}{3\cdot4\cdot7c}-\frac{2}{4b}\cdot\frac{3\cdot5\cdot7c}{3\cdot5\cdot7c}+\frac{1}{7c}\cdot\frac{3\cdot4\cdot5b}{3\cdot4\cdot5b}+\dfrac{7}{21c}\cdot\frac{4\cdot5b}{4\cdot5b}=\)

\(\displaystyle \frac{42c+200b}{420bc}=\frac{100b+21c}{210bc}\)
 

harpazo

Pure Mathematics
Banned
Mar 20, 2018
5,788
361
83
NYC
Simplify

@MarkFL @harpazo this seems like this might go on forever.

\(\displaystyle \dfrac{3}{5b} - \dfrac{2}{4b} + \dfrac{1}{7c} + \dfrac{7}{21c}\)

\(\displaystyle \dfrac{-2}{4b} + \dfrac{1}{7c}\)

\(\displaystyle \dfrac{(-2)(7c) + (4b)(1)}{(4b)(7c)} = \dfrac{(-2)(7c)}{(4b)(7c)} + \dfrac{(4b)(1)}{(4b)(7c)}\)

Cancel out stuff.

\(\displaystyle \dfrac{-2}{4b} + \dfrac{1}{7c}\)

\(\displaystyle \dfrac{3}{5b} -\dfrac{2}{4b} + \dfrac{1}{7c}+ \dfrac{7}{21c}\)
What is the LCD? When you figure that out, then multiply every term by the LCD.
 

MarkFL

La Villa Strangiato
Staff member
Administrator
Moderator
Math Helper
Jan 25, 2018
3,495
4,276
113
St. Augustine
What is the LCD? When you figure that out, then multiply every term by the LCD.
That's not a good strategy unless you have an equation and can do the same thing to both sides.
 

harpazo

Pure Mathematics
Banned
Mar 20, 2018
5,788
361
83
NYC
That's not a good strategy unless you have an equation and can do the same thing to both sides.
Thank you for correcting me.