Y-Δ resistor transfiguration problem

Let ${R_{A}, R_{B}, R_{C}}$ be the resistors of a Y configuration and ${R_{1}, R_{2}, R_{3}}$ the resistors of a Δ configuration. By the required resistors equalities, the following system of equations can be written:

$\frac{{{R_1} \cdot \left( {{R_2} + {R_3}} \right)}}{{{R_1} + {R_2} + {R_3}}} = {R_A} + {R_B},$

$\frac{{{R_2} \cdot \left( {{R_1} + {R_3}} \right)}}{{{R_1} + {R_2} + {R_3}}} = {R_C} + {R_B},$

$\frac{{{R_3} \cdot \left( {{R_1} + {R_2}} \right)}}{{{R_1} + {R_2} + {R_3}}} = {R_A} + {R_C}.$

Transfiguration is a process in which a configuration of resistors is being transformed into a different configuration allowing to simplify electrical circuits. Express ${R_{1}, R_{2}, R_{3}}$ in terms of ${R_{A}, R_{B}, R_{C}}$ . Completing such task will result in a system of formulas with which we can perform Y-Δ transfiguration and thus simplify any given resistor configuration within an electrical circuit. Given options are in terms of ${R_{1}}$ , hence it shows that right steps have been followed. Showing your work would, of course, be appreciated.