Verified answer

Step 1: square both sides

x - 3 + 2x + 1 + 2√((x-3)(2x+1)) = 3x + 4

Step 2: gather like terms

3x -2 + 2√((x-3)(2x+1)) = 3x + 4

Step 3: add -(3x -2) to both sides

2√((x-3)(2x+1)) = 6

Step 4: divide both sides by 2 to simplify as much as possible

√((x-3)(2x+1)) = 3

Step4: square both sides to get rid of √(,,,,)

(x-3)(2x+1) = 9

Step 4: distribute and add -9 to both sides

2x^2 -6x +x - 3 -9 = 0

Step 5: gather like terms

2x^2 -5x -12 = 0

Step 6: factor

(x -4)(2x + 3) = 0

Step 7: solve

x = 4 or x = -3/2

Square both sides to cancel off the square roots:

[√(x-3) + √(2x+1)] [√(x-3) + √(2x+1)] = 3x + 4

Expand the brackets using the foil method:

x - 3 + 2√(x-3)(2x+1) + 2x + 1 = 3x + 4

Add the like terms:

3x - 2 + 2√(x-3)(2x+1) = 3x + 4

Subtract 3x from both sides:

-2 + 2√(x-3)(2x+1) = 4

Add 2 to both sides:

2√(x-3)(2x+1) = 6

Divide both sides by 2:

√(x-3)(2x+1) = 3

Square both sides to cancel off the square root:

(x-3)(2x+1) = 9

Expand the brackets using the foil method:

2x^2 - 5x - 3 = 9

Subtract 9 from both sides:

2x^2 - 5x - 12 = 0

Factor it out:

(2x + 3) (x - 4) = 0

x = 4, - 3/2

shall we assume the question is (2x-a million)/(x+4) = (x+3)/(3x-4) Multiply both part by technique of (x+4) and (3x-4) bypass multiply (2x-a million) (3x-4) = (x+3)(x+4) 6x^2 -11x + 4 = x^2 + 7x +12 convey jointly words 5x^2 -18x - 8 = 0 component (5x + 2)(x - 4) = 0 5x + 2 = 0 or x - 4 =0 x = -2/5 or 4

√(x - 3) + √(2x + 1) = √(3x + 4)

[√(x - 3) + √(2x + 1)]^2 = (3x + 4)

[(x - 3) + 2√((x - 3)(2x + 1)) + (2x + 1)] = (3x + 4)

[3x - 2 + 2√(2x^2 - 5x - 3)] = (3x + 4)

[2√(2x^2 - 5x - 3)] = 6

√(2x^2 - 5x - 3) = 3

2x^2 - 5x - 3 = 9

2x^2 - 5x - 12 = 0

(x - 4)(2x + 3) = 0

Solutions:

x = -3/2

x = 4