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d) \frac{a x}{b} - \frac{b y}{a} = a + b \quad a x - b y = \(2 a b\

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Find derivatives using the quotient rule I

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Q. d) \frac{a x}{b} - \frac{b y}{a} = a + b \quad a x - b y = \(2 a b\

Rewrite Equations: First, let's rewrite the equations to make them easier to work with. $\newline$ Equation (d) becomes $\frac{ax}{b} - \frac{by}{a} = a + b$ . $\newline$ The second equation is already simplified: $ax - by = 2ab$ .
Multiply by $ab$ : Now, let's multiply the first equation by $ab$ to get rid of the fractions. $a^2x - b^2y = a^2b + ab^2.$
Multiply by $b$ : Next, let's multiply the second equation by $b$ to make the coefficients of $x$ the same in both equations. $\newline$ $b \cdot a x - b \cdot b y = b \cdot 2 a b$ . $\newline$ This simplifies to $a \cdot b \cdot x - b^2 \cdot y = 2 a \cdot b^2$ .
System of Equations: Now we have a system of two equations with the same coefficient for $x$ : $\newline$ $1$ . $a^2x - b^2y = a^2b + ab^2$ $\newline$ $2$ . $abx - b^2y = 2ab^2$ .
Subtract and Solve for x: Subtract the second equation from the first to solve for x. $(a^2\cdot x - a\cdot b\cdot x) = (a^2\cdot b + a\cdot b^2) - (2a\cdot b^2)$ . This simplifies to $a\cdot b\cdot x = a^2\cdot b - a\cdot b^2$ .

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