What is expand ((A+B)x+4A+3B)/((x+3)(x+4)) ?

The solution to expand ((A+B)x+4A+3B)/((x+3)(x+4)) is (Ax+Bx+4A+3B)/(x^2+7x+12)

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expand ((A+B)x+4A+3B)/((x+3)(x+4))

expand

\frac{( A + B ) x + 4 A + 3 B}{( x + 3 ) ( x + 4 )}

\frac{A x + B x + 4 A + 3 B}{x ^{2} + 7 x + 12}

Solution steps

\frac{( A + B ) x + 4 A + 3 B}{( x + 3 ) ( x + 4 )}

Expand

(x + 3) (x + 4) : x^{2} + 7 x + 12

= \frac{x ( A + B ) + 4 A + 3 B}{x ^{2} + 7 x + 12}

Expand

(A + B) x + 4 A + 3 B : A x + B x + 4 A + 3 B

= \frac{A x + B x + 4 A + 3 B}{x ^{2} + 7 x + 12}

\frac{1}{( s + 18 ) ^{2}}

\frac{u ^{2} + v ^{2}}{( u - v ) ( u + v )}

\frac{( x - 2 ) ( x + 3 )}{( x - 1 ) ( x + 2 )}

(e^{2} + 1) u^{2}

\frac{\partial}{\partial r} ((x) (r + s))

What is expand ((A+B)x+4A+3B)/((x+3)(x+4)) ?
The solution to expand ((A+B)x+4A+3B)/((x+3)(x+4)) is (Ax+Bx+4A+3B)/(x^2+7x+12)