Need help solving these Algebra problems

Question

a. (x+4/(2x-1)+3/x=21/2x^2-x

b. -13=|2x+4|-5

c. 7=2m^2-3m

d. √4y+7-y=1

e. y^4-7y^2+12=0

Answer 1

a) Multiply through by 2x²-x:

x²+4x+6x-3=21,

x²+10x-24=(x+12)(x-2)=0, so x=-12 or 2.

CHECK: (-8)/(-25)+3/(-12)=8/25-1/4=(32-25)/100=7/100; 21/(288+12)=21/300=7/100.

6/3+3/2=7/2; 21/6=7/2.

b) |2x+4|=-8. No solution because absolutes can't be negative.

c) 2m²-3m-7=0; m=(3±√(9+56))/4=(3±√65)/4; m=(3+√65)/4 or (3-√65)/4.

d) √(4y+7)=y+1, 4y+7=y²+2y+1, y²-2y=6, y²-2y+1=7, (y-1)²=7, y=1±√7. However, y=1-√7 doesn't satisfy the original equation, so solution is y=1+√7.

e) y⁴-7y²+12=0=(y²-4)(y²-3), y=±2 or ±√3 (4 possible solutions).