Rearranging Equations where the term seems to cancel?

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The discussion centers on the algebraic manipulation required to isolate the variable t in an equation involving fractions. The participant struggled with the concept of terms seemingly canceling out, which led to confusion in solving the equation. A key insight was provided by another user, emphasizing the importance of factoring out t instead of attempting to cancel it directly. This approach clarified the misunderstanding and highlighted the necessity of recognizing the relationship between terms in algebraic fractions.

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NovicePWizzard
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So, on a recent maths paper I sat, there was a question where we had to make t the subject. (Disclaimer, this is not homework. I am simply curious, and cannot see how it works. Please don't Ban me) I could not do it for the life of me, because, seemingly the two ts cancel? I know this shouldn't happen, and my teacher went through it, however I've tried it every which way, and the solution still eludes me.
gLYVTSL.jpg

So I tried the following working, which my teacher suggested:
vHQecCg.jpg

So, I began by combining the fraction on the left, then I cross multiplied, collected all terms with t and... What? I can't seem to get any further, without cancelling, let alone getting rid of the b and R.

Am I seriously missing a trick here? I've never really been that good with algebraic fractions.

Also, any tips on the matter would be well received.
 
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NovicePWizzard said:
So, on a recent maths paper I sat, there was a question where we had to make t the subject. (Disclaimer, this is not homework. I am simply curious, and cannot see how it works. Please don't Ban me) I could not do it for the life of me, because, seemingly the two ts cancel? I know this shouldn't happen, and my teacher went through it, however I've tried it every which way, and the solution still eludes me.
gLYVTSL.jpg

So I tried the following working, which my teacher suggested:
vHQecCg.jpg

So, I began by combining the fraction on the left, then I cross multiplied, collected all terms with t and... What? I can't seem to get any further, without cancelling, let alone getting rid of the b and R.

Am I seriously missing a trick here? I've never really been that good with algebraic fractions.

Also, any tips on the matter would be well received.

Why not factor out the t and then divide? The t's wouldn't cancel out anyway, there's no way to do that.
 
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Student100 said:
Why not factor out the t and then divide? The t's wouldn't cancel out anyway, there's no way to do that.
OHHHHHHHHHHHH

Thank you! That makes so much sense and I feel really dumb now. I guess I forget sometimes that -Rt = -1*R*t and thus I can factor it out like that.
 

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