simplify complex fractions......

Princezz3286

Junior Member
the directions are to simplify completely.....
I am not too sure how to write these so you can see what the problem looks like exactally....... but I'll try to explain it......
1) 1+ 2/d -3
---------------
-2d/ d-3 - d

This problem reads 1 + 2 over (d -3), all over -2d over (d - 3). the -d is written after the fraction. I hope this kind of makes sense...... in my book it say the answer is -1/d but I keep getting something completely different....

to begin, on the top I multiply the 1/1 by (d - 3) to get the lcd so I can add them and then I can cancel the d - 3 from the top and the bottom and I am left with 2

for the bottom part..... I multiplied (-2d/d - 3) by d and I multiplied the (- d) by (d - 3) to get the lcd d(d - 3)
I got -d (2d) / d(d - 3) minus d (d - 3) so I end up with - d (2d) - d (d - 3)/ d (d - 3) and cancel the d (d - 3)
I get for the final simplification, - 2/ d (2d) where nothing can be cancelled or combined as they are not like terms.... but the answer in my book is - 1/d can someone please highlight what I did wrong here? I really struggle with these types of problems.......

jwpaine

Full Member
$$\displaystyle \frac{\frac{1+2}{d -3} }{ \frac{-2d}{d-3}-d}$$

First, make the denominator into a single rational, recall: $$\displaystyle \frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{db}$$

$$\displaystyle \frac{-2d}{d-3}-d} = \frac{-2d - d(d-3)}{(d-3)} = \frac{-2d -d^2 + 3}{(d-3)}$$ (don't factor yet, it'll be easier)

Now multiply the numerator of the original rational by the reciprocal of your new denominator. Recall: $$\displaystyle \frac{\frac{a}{b}}{c} = \frac{a}{b} x \frac{1}{c}$$

$$\displaystyle \frac{(1+2)}{(d -3)} \cdot \frac{(d-3)}{-2d -d^2 + 3}$$

Now you can cancel the (d-3) from both the numerator and denom.... then proceed to factor and cancel some more!

John

Princezz3286

Junior Member
in regards to this problem, does it matter that the top equation in my book had the 1 + in front of the fraction on the top? I noticed that you had it written correctly all except that...... Sorry for so many questions but I get really lost on these...... I am horrible at math in case you hadn't noticed!

Heather

jwpaine

Full Member
Yes, it would matter.

Hopefully my above work can guide you in the right direction for the 1 being added to a rational.

John