My Math Forum Making a letter the subject of an equation

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 February 26th, 2017, 04:52 AM #1 Newbie   Joined: Feb 2017 From: uk Posts: 6 Thanks: 0 Making a letter the subject of an equation Hey guys, I've been studying maths for a few months but I'm really struggling with making a letter the subject when it is on both sides of the equations (in a fraction) i.e. please see below (how would i make t the subject)? The part I struggle with is removing t from one side (there is only '1' 't' on either side so how do i get rid of one without removing the other?) 5y - 11/t = 13 - 7y/t Any help is much appreciated
 February 26th, 2017, 05:00 AM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 2,425 Thanks: 1194 $5y-\dfrac{11}{t}=13-\dfrac{7y}{t}$ start by multiplying every term by $t$ ... $5yt-11=13t-7y$ move all terms with a factor of $t$ to the same side, all terms w/o to the other side ... $5yt -13t=11-7y$ factor out $t$ ... $t(5y-13)=11-7y$ divide both sides by $5y-13$ ... $t=\dfrac{11-7y}{5y-13}$ Thanks from tenpence
 February 26th, 2017, 05:04 AM #3 Newbie   Joined: Feb 2017 From: uk Posts: 6 Thanks: 0 Thank you so much!!!
 March 3rd, 2017, 04:59 AM #4 Math Team   Joined: Jan 2015 From: Alabama Posts: 2,343 Thanks: 589 Equivalently, starting with $5y- \frac{11}{t}= 13- \frac{7y}{t}$ add $\frac{11}{t}$ to both sides: $5y= 13-\frac{7y}{t}+ \frac{11}{t}= 13+ \frac{11- 7y}{t}$ Subtract 13 from both sides: $5y- 13= \frac{11- 7y}{t}$ Invert both sides: $\frac{1}{5y- 13}= \frac{t}{11- 7y}$ Finally, multiply both sides by 11- 7y: $\frac{11- 7y}{5y- 13}= t$

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