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simplify 4/(2x+1) - 2/(5x-1) as a fraction?

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1 Answer

For converting this to a fraction, we need to combine the two terms in the equation into a single term. This is done by making denominators of both the terms same and then subtracting the numerators.
For making the denominator same, we need to find the Least Common Multiple (LCM) of (2x+1) and (5x-1), which is (2x+1)(5x-1).
So multiply and divide the first term by (5x-1) and multiply and divide the second term by (2x+1) to get the LCM in the denominator.
4/(2x+1) - 2/(5x-1)
= 4/(2x+1)*(5x-1)/(5x-1) - 2/(5x-1)*(2x+1)/(2x+1)
Now simplify to get the LCM in the denominator
= 4(5x-1)/(2x+1)(5x-1) - 2(2x+1)/(2x+1)(5x-1)
= (20x-4)/(2x+1)(5x-1) - (4x+2)/(2x+1)(5x-1)
Since denominators of both terms are same LCM, we can subtract numerators of two fractions
=((20x-4)-(4x+2))/(2x+1)(5x-1)
= (20x-4-4x-2)/(2x+1)(5x-1)
= (16x-6)/(2x+1)(5x-1)
Take out common factor 2 from the numerator
= 2(8x-3)/(2x+1)(5x-1) This is the fraction.