Question 1 Report
Solve the following equation \( \frac{2}{2r-1} - \frac{5}{3} = \frac{1}{r+2} \)
Answer Details
22r−1 2 2 r − 1 - 53 5 3 = 1r+2 1 r + 2 22r−1 2 2 r − 1 - 1r+2 1 r + 2 = 53 5 3 2r+4−2r+12r−1(r+2) 2 r + 4 − 2 r + 1 2 r − 1 ( r + 2 ) = 53 5 3 5(2r+1)(r+2) 5 ( 2 r + 1 ) ( r + 2 ) = 53 5 3 5(2r - 1)(r + 2) = 15 (10r - 5)(r + 2) = 15 10r2 + 20r - 5r - 10 = 15 10r2 + 15r = 25 10r2 + 15r - 25 = 0 2r2 + 3r - 5 = 0 (2r2 + 5r)(2r + 5) = r(2r + 5) - 1(2r + 5) (r - 1)(2r + 5) = 0 r = 1 or −52
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