Rearranging Equations where the term seems to cancel?

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The discussion centers on a math problem involving rearranging an equation to make 't' the subject, where the participant struggles with seemingly canceling terms. Despite following their teacher's advice to combine fractions and cross-multiply, they find themselves unable to proceed without canceling terms, which they know is incorrect. A suggestion to factor out 't' clarifies the misunderstanding, highlighting that 't' cannot simply cancel out in the equation. The participant expresses relief upon understanding this method, realizing that factoring allows for proper manipulation of the equation. This interaction emphasizes the importance of recognizing algebraic principles in solving equations.
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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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