Question

Simplify x/(2x+3) - 4/(5x-1)

Answer 1

The easiest way to simplify is to combine both fractions into a common denominator.

I suggest using the "cross-multiply / straight multiply" method. Consider this example:

\[\frac23-\frac45=\frac{2*5-4*3}{3*5}=\frac{10-12}{15}=\frac{-2}{15}\]

See how you "cross-multiply" numerators & denominators to create the new numerator in the combined fraction, but you multiply "straight-across" the denominators to get the new denominator?

Try this with the expression you have and see what you get. Keep in mind you have to distribute carefully!

Answer 2

So does if simplify to5x^2-9x-12/(2x+3)(5x-1)

Answer 3

Yes, that looks correct. Well done!