Latex Test

    \[ \begin{array}{llll} R_{1} &=\qquad  \dfrac{wl}{2} &\qquad\\ R_{2} &=\qquad  R{_{1}} &\qquad\\ V_{x} &=\qquad  w\left(\dfrac{l}{2}-x\right) &\qquad\\ V_{\max} &=\qquad  R{_{1}}=R{_{2}} &\qquad & \text{at}\;R_{1}\;\text{and}\;R_{2}\\ M_{\max} &=\qquad \dfrac{wl^{2}}{8} &\qquad & \text{at centre} \\ M_{x} &=\qquad \dfrac{wx}{2}\left(l-x\right) &\qquad\\ \delta_{\max} &=\qquad \dfrac{5wl^{4}}{384EI} &\qquad & \text{at centre} \\ \delta_{x} &=\qquad \dfrac{wx}{24EI}\left(l^{3}-2lx^{2}+x^{3}\right) &\qquad \end{array} \]

    \[ \begin{array}{llll} R_{1} &=\qquad V_{1}&\qquad& \text{max when}\;a<c\; \\ &=\qquad \dfrac{wb}{2l}\left(2c+b\right) &\qquad& \\ R_{2} &=\qquad V_{2} &\qquad& \text{max when}\;a>c\\  &=\qquad \dfrac{wb}{2l}\left(2a+b\right) &\qquad& \\ V_{x} &=\qquad R_{1}-w\left(x-a\right)&\qquad& \text{when}\;x>a\;\text{ and}\;x<(a+b) \\ M_{\max} &=\qquad R_{1}\left(a+\dfrac{R_{1}}{2w}\right)&\qquad& \text{at}\;x=a+\dfrac{R_{1}}{w}\\ M_{x} &=\qquad R_{1}x &\qquad& \text{when}\;x<a \\ M_{x} &=\qquad R_{1}x-\dfrac{w}{2}\left(x-a\right)^{2} &\qquad& \text{when}\;x>a\;\text{ and}\;x<(a+b) \\ M_{x} &=\qquad R_{2}\left(l-x\right) &\qquad& \text{when}\;x>(a+b) \end{array} \]

    \[ \begin{array}{llll} R_{1} &=\qquad V_{1}&\qquad& \\ &=\qquad \dfrac{wa}{2l}\left(2l-a\right) &\qquad& \\ R_{2} &=\qquad V_{2} &\qquad& \\ &=\qquad \dfrac{w{a}^{2}}{2l}&\qquad& \\ V_{x} &=\qquad R_{1}-wx&\qquad& \text{when}\;x<a\\ M_{\max} &=\qquad \dfrac{{R_{1}}^{2}}{2w}&\qquad& \text{at}\;x=\dfrac{R_{1}}{w}\\ M_{x} &=\qquad R_{1}x-\dfrac{w{x}^{2}}{2}&\qquad& \text{when}\; x<a\\ M_{x} &=\qquad R_{2}\left(l-x\right) &\qquad& \text{when}\; x>a\\ \delta_{x} &=\qquad \dfrac{wx}{24EIl}\left(a^{2}(2l-a)^{2}-2ax^{2}(2l-a)+lx^{3}\right)&\qquad& \text{when}\; x<a\\ \delta_{x} &=\qquad \dfrac{wa^{2}(l-x)}{24EIl}\left(4xl-2x^{2}-a^{2}\right)&\qquad& \text{when}\; x>a \end{array} \]

    \[ \begin{array}{llll} R_{1} &=\qquad V_{1}&\qquad& \\ &=\qquad \dfrac{w_{1}a(2l-a)+w_{2}c^{2}}{2l}&\qquad& \\ R_{2} &=\qquad V_{2} &\qquad& \\ &=\qquad \dfrac{w_{2}c(2l-c)+w_{1}a^{2}}{2l}&\qquad& \\ V_{x} &=\qquad R_{1}-w_{1}x&\qquad& \text{when}}\;x<a\\ V_{x} &=\qquad R_{1}-w_{1}a&\qquad& \text{when}\;x>a\;\text{ and}\;x<(a+b)\\ V_{x} &=\qquad R_{1}-w_{2}(l-x)&\qquad& \text{when}\; x>a+b\\ M_{\max} &=\qquad \dfrac{{R_{1}}^{2}}{2w_{1}}&\qquad& \text{at}\;x=\dfrac{R_{1}}{w_{1}}\;\text{when}\;R_{1}<w_{2}a\\ M_{\max} &=\qquad \dfrac{{R_{2}}^{2}}{2w_{2}}&\qquad& \text{at}\;x=l-\dfrac{R_{2}}{w_{2}}\;\text{when}\;R_{2}<w_{2}c\\ M_{x} &=\qquad R_{1}x-\dfrac{w_{1}x^{2}}{2}&\qquad& \text{when}\; x<a\\ M_{x} &=\qquad R_{1}x-\dfrac{w_{1}a}{2}(2x-a)&\qquad& \text{when}\;x>a\;\text{ and}\;x<(a+b)\\ M_{x} &=\qquad R_{2}(l-x)-\dfrac{w_{2}(l-x)^{2}}{2}&\qquad& \text{when}\; x>(a+b) \end{array} \]