Rearranging Equations where the term seems to cancel?

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In summary, the question discussed was regarding making t the subject in a recent maths paper. The individual was unable to solve it due to the apparent cancellation of two t's. However, after trying various methods and seeking advice from their teacher, they realized that they could factor out the t and continue solving the equation. The individual also requested any tips on the matter.
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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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  • #2
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.
 

1. How do I solve for a variable when it appears on both sides of the equation?

This is a common question when trying to rearrange equations with cancelling terms. To solve for a variable, you need to isolate it on one side of the equation by performing inverse operations. For example, if you have the equation 2x + 3 = 9, you can solve for x by first subtracting 3 from both sides to get 2x = 6. Then, divide both sides by 2 to get x = 3.

2. What if the terms cancelling are not the same?

In this case, you need to use the distributive property to factor out the common term. For example, if you have the equation 2x + 6 = 4x + 12, you can factor out 2 on the left side to get 2(x + 3) = 4x + 12. Then, you can continue solving for x by isolating it on one side of the equation.

3. Can I cancel out terms in fractions?

Yes, you can cancel out terms in fractions as long as they are in the same numerator or denominator. For example, if you have the equation 3x/5 = 21/35, you can cancel out the common factor of 7 on both sides to get x/5 = 3/5. Then, multiply both sides by 5 to solve for x.

4. What happens if I have a negative term that cancels out?

If you have a negative term that cancels out, you can simply treat it as a positive term. For example, if you have the equation 2x - 6 = -2x + 12, you can cancel out the -2x terms to get 4x = 18. Then, solve for x as usual.

5. Is there a certain order I should follow when rearranging equations?

Yes, it is important to follow the order of operations when rearranging equations. This means performing any operations inside parentheses first, then exponents, then multiplication and division from left to right, and finally addition and subtraction from left to right. Following this order will ensure that you get the correct solution for your equation.

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