Prove equivalent fractions with $\pm $ sign

If

$\lambda =\frac{{n}_{1}}{{n}_{2}}=\frac{{m}_{1}}{{m}_{2}}$

prove that

$\lambda =\frac{{n}_{1}\pm {m}_{1}}{{n}_{2}\pm {m}_{2}}$

I know this is true if I add numbers to it

$\frac{1}{2}=\frac{2}{4}$

$\frac{1+2}{2+4}=\frac{3}{6}=\frac{1}{2}$

$\frac{1-2}{2-4}=\frac{-1}{-2}=\frac{1}{2}$

If

$\lambda =\frac{{n}_{1}}{{n}_{2}}=\frac{{m}_{1}}{{m}_{2}}$

prove that

$\lambda =\frac{{n}_{1}\pm {m}_{1}}{{n}_{2}\pm {m}_{2}}$

I know this is true if I add numbers to it

$\frac{1}{2}=\frac{2}{4}$

$\frac{1+2}{2+4}=\frac{3}{6}=\frac{1}{2}$

$\frac{1-2}{2-4}=\frac{-1}{-2}=\frac{1}{2}$