Question

SOLVING ALGEBRAIC FRACTIONS please explain , I’m so confused

Answer 1

`(x)/(2x - 3) + (4)/(x + 1) = 1\:(x\\eq -1,x\\eq (3)/(2)) \\ \Leftrightarrow (x(x + 1) + 4(2x - 3))/((2x - 3)(x + 1)) = ((2x - 3)(x + 1))/((2x - 3)(x + 1)) \\ \Leftrightarrow x(x + 1) + 4(2x - 3) = (2x - 3)(x + 1) \\ \Leftrightarrow {x}^(2) + x + 8x - 12 = 2 {x}^(2) -x - 3 \\ \Leftrightarrow {x}^(2) - 10x + 9 = 0 \\ \Leftrightarrow {x}^(2) - 9x - x + 9 = 0 \\ \Leftrightarrow x(x - 9) - (x - 9) = 0 \\ \Leftrightarrow (x - 9)(x - 1) = 0 \\ \Leftrightarrow x = 1 \: \vee \: x = 9`