simplify the exspressions and solve the equations 7 1t13t314

simplify the exspressions and solve the equations.

7. 1/t-1-3/t-3=1/4

8.4x^2-x-14/x-2divided by4x^2+x-14/x+2

9 .z^2-3z+2/z@+3z-4 multiplied byz^2+6z+8/z^2-4=z

10. 2h^2-2h-4/(h+1)(h-2)+h^2+h-2/(h+2)(h-1)

Solution

7)(1/(t-1)) -(3/(t-3))=1/4

convert 2 sikmple fractions to compound fraction

(1(t-3) -3(t-1))/((t-1)(t-3))=1/4

(t-3-3t+3)/((t-1)(t-3))=1/4

(-2t)/((t-1)(t-3))=1/4

cross multiply

(-2t)*4=(t-1)(t-3)

-8t =t²-4t+3

t²-4t+3+8t=0

t²+4t+3=0

t²+3t+t+3=0

t(t+3)+1(t+3)=0

(t+1)(t+3)=0

t+1=0,t+3=0

t=-1 ,t=-3