Question

solve for x(4x/(x-2) -3x/(x-1) =7 1/2)​

Answer 1

Answer:

solution x[4x²-4x-3x²+6x]/x²-x-2x+2=15/2

x[x²+2x]/x²-3x+2=15/2

[x³+2x²]/x²-3x+2=15/2

2x³+4x²=15x²-45x+30

2x³-11x²+45x-30=0

Answer 2

Step-by-step explanation:

$\bf \frac{4x}{(x-2) }- \frac{3x}{(x-1)} =7 \frac{1}{2} \\ \\ \bf \frac{4x}{(x-2) }- \frac{3x}{(x-1)} = \frac{15}{2} \\ \\ \bf \frac{4x(x - 1) - 3x(x - 2)}{(x-2)(x-1)} = \frac{15}{2} \\ \\ \bf \frac{4 {x}^{2} - 4x- 3 {x}^{2} + 6x}{ {x}^{2} - 3x + 2 } = \frac{15}{2} \\ \\ \bf \frac{ {x}^{2} + 2x}{ {x}^{2} - 3x + 2 } = \frac{15}{2} \\ \\ \bf2 {x}^{2} + 4x = 15 {x}^{2} - 45x + 30 \\ \\ \bf13 {x}^{2} - 49x + 30 = 0 \\ \\ \bf13 {x}^{2} - 39x - 10x + 30 = 0 \\ \\ \bf13 {x}(x - 3) - 10(x - 3) = 0 \\ \\ \bf(x - 3)(13x - 10) = 0 \\ \\ \large \leadsto\blue{ \boxed{ \pmb {\tt{x= 3 \: \: or \: \: \frac{10}{13} }}}}$