If the equations $2 a x^2-3 b x+4 c=0$ and $3 x^2-4 x+5=0$ have a common root, then $\frac{a+b}{b+c}$ is equal to $(a, b, c \in \boldsymbol{R})$

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If the equations $2 a x^2-3 b x+4 c=0$ and $3 x^2-4 x+5=0$ have a common root, then $\frac{a+b}{b+c}$ is…