Question

solución de esta ecuación 4x-1/x-1 + 1 = 5/4

Answer 1

4x-1/x-1 + 1 = 5/4

4x-1/x-1 = 5/4 + 1

4x-1/x-1 = 1/4

4(4x-1) = x-1

16x - 4 = x - 1

16x - x = 4-1

15x = 3

x=1/5

Answer 2

Respuesta:

$x=[\frac{5-\sqrt{281} }{32} , \frac{5+\sqrt{281}}{32}]=[-0.3675954566950066,0.6800954566950066]$

Explicación paso a paso:

$4x-\frac{1}{x} -1+1=\frac{5}{4}\\\\4x-\frac{1}{x}=\frac{5}{4}\\\\4x=\frac{5}{4}+\frac{1}{x}\\\\4x=\frac{5*x}{4*x}+\frac{1*4}{x*4}\\\\4x=\frac{5x+4}{4x}\\\\4x*4x=5x+4\\\\16x^{2} =5x+4\\\\16x^{2}-5x-4=0$

Ahora se resuelve una función cuadrática:

$a=16\\b=-5\\c=-4\\\\x=[\frac{-b-\sqrt{b^{2}-4ac} }{2a} , \frac{-b+\sqrt{b^{2}-4ac} }{2a}]\\\\x=[\frac{-(-5)-\sqrt{(-5)^{2}-4(16)(-4)} }{2(16)} , \frac{-(-5)+\sqrt{(-5)^{2}-4(16)(-4)} }{2(16)}]\\\\x=[\frac{5-\sqrt{25+256} }{32} , \frac{5+\sqrt{25+256} }{32}]\\\\x=[\frac{5-\sqrt{281} }{32} , \frac{5+\sqrt{281}}{32}]$