How to simplify an expression by substituting a ratio of variables by a new variable?

Question:How to simplify an expression by substituting a ratio of variables by a new variable?

Posted: zenterix 400 Product: Maple 2022

February 05 2025

I'd like to simplify the simple expression below by dividing numerator and denominator by m_1 to obtain an expression only containing alpha.

Maple doesn't not generate the desired result.

Is there a way to do this?

expr := sqrt(-(-m__1-m__2+sqrt(m__2*(m__1+m__2)))*`ω__0`^2/m__1)

(-(-m__1-m__2+(m__2*(m__1+m__2))^(1/2))*omega__0^2/m__1)^(1/2)

(1)

$simplify(expr, {m__2/m__1 = alpha})$

(omega__0^2*(alpha*m__1+m__1-(m__1^2*alpha*(alpha+1))^(1/2))/m__1)^(1/2)

(2)

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