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Simplify x/(2x+3) - 4/(5x-1)
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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!
So does if simplify to5x^2-9x-12/(2x+3)(5x-1)
Yes, that looks correct. Well done!
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