Solve the equation: (4r−3)/(6r+1) = (2r−1)/(3r+4)

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ScanSolve AI Tutor · Accepted Answer

Step 1: Cross-multiply the fractions. Given the equation: (4r−3)/(6r+1) = (2r−1)/(3r+4) Multiply both sides by (6r+1)(3r+4) to eliminate the denominators: (4r−3)(3r+4) = (2r−1)(6r+1) Step 2: Expand both sides of the equation. Expand the left side: 4r(3r) + 4r(4) − 3(3r) − 3(4) = 12r² + 16r − 9r − 12 = 12r² + 7r − 12 Expand the right side: 2r(6r) + 2r(1) − 1(6r) − 1(1) = 12r² + 2r − 6r − 1 = 12r² − 4r − 1 Now the equation is: 12r² + 7r − 12 = 12r² − 4r − 1 Step 3: Rearrange the terms to solve for r. Subtract 12r² from both sides: 7r − 12 = −4r − 1 Add 4r to both sides: 7r + 4r − 12 = −1; 11r − 12 = −1 Add 12 to both sides: 11r = −1 + 12; 11r = 11 Divide by 11: r = 11/11; r = 1 Step 4: Check for excluded values. The denominators cannot be zero. 6r+1 ≠ 0 ⇒ 6r ≠ −1 ⇒ r ≠ −1/6 3r+4 ≠ 0 ⇒ 3r ≠ −4 ⇒ r ≠ −4/3 Since r=1 is not equal to −1/6 or −4/3, it is a valid solution. The solution is r=1.

Solve the equation: (4r-3)/(6r+1) = (2r−1)/(3r+4)

Answer

Step-by-step solution

Cross-multiply the fractions.

Expand both sides of the equation.

Rearrange the terms to solve for $r$ .

Check for excluded values.

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