There are two infinitely long straight current-carrying conductors...

$B = \dfrac{{\mu}_{0}I}{4\pi y}\left(1 + sin{\theta}_{1}\right) + \dfrac{{\mu}_{0}I}{4\pi x}\left(1 + sin{\theta}_{2}\right)$
$B = \dfrac{{\mu}_{0}I}{4\pi y}\left(1 + \dfrac{x}{\sqrt{{x}^{2} + {y}^{2}}}\right) + \dfrac{{\mu}_{0}I}{4\pi x}\left(1 + \dfrac{y}{\sqrt{{x}^{2} + {y}^{2}}}\right)$

$B = \dfrac{{\mu}_{0}I}{4\pi x} + \dfrac{{\mu}_{0}I}{4\pi y} + \dfrac{{\mu}_{0}I}{4\pi}\left[\dfrac{x}{y\sqrt{{x}^{2} + {y}^{2}}} + \dfrac{y}{x\sqrt{{x}^{2} + {y}^{2}}}\right] ⇒ B = \dfrac{{\mu}_{0}I}{4\pi}\left[\dfrac{1}{x} + \dfrac{1}{y}\right] + \dfrac{{\mu}_{0}I}{4\pi}\dfrac{\sqrt{{x}^{2} + {y}^{2}}}{xy} = \dfrac{{\mu}_{0}I}{4\pi}\left[\dfrac{x + y + \sqrt{{x}^{2} + {y}^{2}}}{xy}\right]$