Answer:
I can only assume that the entire 1-4x is divided by 2x, and 4 by all of 1 - 5x. You can guarantee more accurate results by using brackets where appropriate. If I read that expression with the correct notation, it reads as [tex]1 - \frac{4x}{2x} + 1 = \frac{4}{1} - 5x[/tex].
Assuming instead that it's meant as [tex]\frac{1 - 4x}{2x + 1} = \frac{4}{1 - 5x}[/tex], we can solve it as shown below, giving us x values of 1 and 3/20 (or 0.15).
Step-by-step explanation:
First let's reformat this to the usual ax² + bx + c format:
[tex]\frac{1 - 4x}{2x + 1} = \frac{4}{1 - 5x}\\(1 - 4x)(1 - 5x) = 4(2x + 1)\\1 - 5x - 4x + 20x^2 = 8x + 4\\20x^2 - 5x - 4x - 8x + 1 - 4 = 0\\20x^2 - 17x - 3 = 0[/tex]
Let's solve it with the quadratic formula:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}\\\\x = \frac{17 \pm \sqrt{-17^2 - 4\times 20 \times( -3)} }{2\times20}\\\\x = \frac{17 \pm \sqrt{289 + 240} }{40}\\\\x = \frac{17 \pm 23 }{40}\\\\x = 1, \frac{3}{20}[/tex]
