Question

1. (a+дробь b-a/1+ab): (1-дробь a(b-a)/1+ab)= 2. (a- дробь 4a-9/a-2): (2a дробь-2a/a-2)= 3. (x+1 -дробь 12x-13/x+3): (x-3- дробь 7/x+3)= решите !

Answer 1

$(a+ \frac{b-a}{1+ab} ):(1- \frac{a(b-a)}{1+ab} )= \frac{a+a ^{2}b+b-a }{1+ab} * \frac{1+ab}{1+ab-ab+ a^{2} } = \frac{b( a^{2}+1) }{1+ a^{2} } =b$
$(a- \frac{4a-9}{a-2} ):(2a- \frac{2a}{a-2} )= \frac{ a^{2} -2a-4a+9}{a-2} * \frac{a-2}{2 a^{2}-4a-2a } = \frac{ a^{2}-6a+9}{2 a^{2} -6a} = \frac{(a-3) ^{2} }{2a(a-3)}$
=(a-3)/2a
$( x+1- \frac{12x-13}{x+3} ):(x-3- \frac{7}{x+3} )= \frac{ x^{2} +4x+3-12x+13}{x+3} * \frac{x+3}{ x^{2} -9-7} =$
$\frac{ x^{2} +8x+16}{ x^{2} -16} = \frac{(x+4) ^{2} }{(x-4)(x+4)} = \frac{x+4}{x-4}$