((x-1)/3x+15))-((x+3)/(5x+25))
HOW TO SIMPLIFY THAT???
To simplify the given expression ((x-1)/3x+15))-((x+3)/(5x+25)), we need to combine the two fractions by finding a common denominator.
Step 1: Find the least common multiple (LCM) of the denominators, which in this case are 3x+15 and 5x+25.
Step 2: Factor both denominators:
For the first denominator, 3x+15, you can factor out 3, giving us 3(x+5).
For the second denominator, 5x+25, you can factor out 5, giving us 5(x+5).
Step 3: Now, we can see that the common denominator is (x+5)(3)(5), which simplifies to 15(x+5).
Step 4: Multiply the numerator of the first fraction ((x-1)) by the common denominator 15(x+5)/(15(x+5)).
Step 5: Multiply the numerator of the second fraction ((x+3)) by the common denominator 3(x+5)/(15(x+5)).
Step 6: Now, we can combine the fractions by subtracting the numerators while keeping the common denominator.
To do that, we have:
((x-1) * 15(x+5) - (x+3) * 3(x+5)) / (15(x+5))
= (15x^2 - 15 + 75x + 375 - 3x^2 - 6x - 15x - 30) / (15(x+5))
= (12x^2 + 54x + 330) / (15x + 75)
Thus, the simplified form of the given expression is (12x^2 + 54x + 330) / (15x + 75).