Answer:
4) a = 6
5) m = 1
Step-by-step explanation:
4) use FOIL, First Inside Outside Last, when you cross multiply.
[tex]\frac{a+4}{a-1} =\frac{a-2}{a-4}[/tex]
[tex](a+4)(a-4) = (a-1)(a-2)[/tex]
I'm going to do the left side first.
[tex](a+4)(a-4)\\a^2-4a+4a-16\\a^2-16[/tex]
Now I'm going to do the right side.
[tex](a-1)(a-2)\\a^2-2a-1a+2\\a^2-3a+2[/tex]
Next I'm going to rewrite back as the equation and solve for a.
[tex]a^2 - 16 = a^2 -3a +2\\a^2 - a^2 -16 = a^2-a^2-3a+2\\-16-2=-3a+2-2\\-18=-3a\\-18/-3=-3a/-3\\a=6[/tex]
5) I'm going to use distributive propoerty when I cross multiply. Then I will setup an equation like number 4 and solve for m.
[tex]\frac{5m-2}{3}=\frac{8-3m}{5} \\[/tex]
[tex]5(5m-2)=3(8-3m)\\25m-10=24-9m\\25m+9m-10=24-9m+9m\\34m-10=24\\34m-10+10=24+10\\34m=34\\34m/34=34/34\\m=1[/tex]
