simplification

[savanahv]

Hello! Sorry about the maybe dumb question. I am a university student taking Calculus 2 next semester. I took calc 1 about 3 years ago but have done hardly any math since then. I have spent the summer trying to relearn calc 1 and I have found that while I'm not struggling with the concepts, I've forgotten A LOT of my more basic arithmetic and algebra skills. I am working on the above question and I have the correct answer however I can't figure out how to simplify it.

The first equation is where I arrived on my own. The second equation shows the simplification I should get but I cant understand how to get from the first equation to the second - particularly how the first fraction in the numerator ended up in the denominator and how the second root x became 2x. Any explanation on simplifying fractions would be awesome.

 

[tkhunny]

"ended up in the denominator" is not a good thing to be wondering. Things obey rules. They don't just jump around.

The only troublesome denominator-looking piece is [math]2\cdot\sqrt{x}[/math] in that first term.

Multiply independently, both numerator and denominator by [math]2\cdot\sqrt{x}[/math].

 

[LCKurtz]

Multiply the fraction by [MATH]1 =\frac {2\sqrt x}{2\sqrt x} [/MATH]. I see someone has already answered but since I have already typed it, here it is.

 

[Deleted member 4993]

View attachment 20984
Hello! Sorry about the maybe dumb question. I am a university student taking Calculus 2 next semester. I took calc 1 about 3 years ago but have done hardly any math since then. I have spent the summer trying to relearn calc 1 and I have found that while I'm not struggling with the concepts, I've forgotten A LOT of my more basic arithmetic and algebra skills. I am working on the above question and I have the correct answer however I can't figure out how to simplify it.
View attachment 20985
The first equation is where I arrived on my own. The second equation shows the simplification I should get but I cant understand how to get from the first equation to the second - particularly how the first fraction in the numerator ended up in the denominator and how the second root x became 2x. Any explanation on simplifying fractions would be awesome.

How would you simplify:

\(\displaystyle \frac{\frac{a}{b}-c}{d} \ \to\ \frac{a - b*c}{b*d} \)

 

[savanahv]

"ended up in the denominator" is not a good thing to be wondering. Things obey rules. They don't just jump around.

The only troublesome denominator-looking piece is [math]2\cdot\sqrt{x}[/math] in that first term.

Multiply independently, both numerator and denominator by [math]2\cdot\sqrt{x}[/math].

Thank you! the bottom two sentences were very helpful, wasn't sure how the first one was necessary but thanks regardless!

 

[savanahv]

Multiply the fraction by [MATH]1 =\frac {2\sqrt x}{2\sqrt x} [/MATH]. I see someone has already answered but since I have already typed it, here it is.

thank you for the help!!

 

[tkhunny]

Thank you! the bottom two sentences were very helpful, wasn't sure how the first one was necessary but thanks regardless!

Part of what you should be learning is philosophy, philosophy of approaching a problem, philosophy of analyzing a problem, philosophy of thinking about a problem, philosophy of recasting a problem. That's why the first sentence was necessary. Don't take it personally. Use it to improve your philosophy. Math isn't just manipulating little symbols; it is a way to think.

 

[savanahv]

Part of what you should be learning is philosophy, philosophy of approaching a problem, philosophy of analyzing a problem, philosophy of thinking about a problem, philosophy of recasting a problem. That's why the first sentence was necessary. Don't take it personally. Use it to improve your philosophy. Math isn't just manipulating little symbols; it is a way to think.

Hey its cool you find math super fascinating but I was just looking for study help hahaha - next time please leave the air of condescension out of helping us simpleton 100-level calc students. Nothing was taken personal I promise

 

[tkhunny]

Hey its cool you find math super fascinating but I was just looking for study help hahaha - next time please leave the air of condescension out of helping us simpleton 100-level calc students. Nothing was taken personal I promise

There was no "air of condescending", so that makes it tough to leave it out. Anyway, let's learn some mathematics.