[tex]\dfrac a b = \dfrac c d[/tex]
Cross multiply,
[tex]ad = bc[/tex]
Add ac to both sides,
[tex]ad + ac = bc + ac[/tex]
Factor,
[tex]a(d+c) = c(b+a)[/tex]
Divide by (b+a)(d+c),
[tex]\dfrac{a}{b+a} = \dfrac{c}{d+c} \quad\checkmark[/tex]
