This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Find a common denominator for the two fractions. The denominators are (x+5) and (3x-4). The least common denominator (LCD) is the product of these two denominators: (x+5)(3x-4). Step 2: Rewrite each fraction with the common denominator. For the first fraction, multiply the numerator and denominator by (3x-4): (2)/(x+5) = (2(3x-4))/((x+5)(3x-4)) For the second fraction, multiply the numerator and denominator by (x+5): (5)/(3x-4) = (5(x+5))/((x+5)(3x-4)) Step 3: Subtract the rewritten fractions. (2(3x-4))/((x+5)(3x-4)) - (5(x+5))/((x+5)(3x-4)) = (2(3x-4) - 5(x+5))/((x+5)(3x-4)) Step 4: Expand the terms in the numerator. 2(3x-4) = 6x - 8 5(x+5) = 5x + 25 Substitute these back into the numerator: (6x - 8) - (5x + 25) Step 5: Simplify the numerator by distributing the negative sign and combining like terms. 6x - 8 - 5x - 25 Combine the x terms: 6x - 5x = x Combine the constant terms: -8 - 25 = -33 The simplified numerator is x - 33. Step 6: Write the expression as a single fraction in its lowest form. The numerator is x-33 and the denominator is (x+5)(3x-4). There are no common factors between the numerator and the denominator, so the fraction is in its lowest form. (x-33)/((x+5)(3x-4)) 3 done, 2 left today. You're making progress.