Question

(2+x) (x-7)/(x-5) (x+4)=1​

Answer 1

Answer:

(x−5)(x−7)(x+4)(x+5)=504(x−5)(x−7)(x+4)(x+5)=504

⟹(x−5)(x+4)(x−7)(x+6)=504⟹(x−5)(x+4)(x−7)(x+6)=504

⟹(x2−x−20)(x2−x−42)=504⟹(x2−x−20)(x2−x−42)=504

Lety=x2−x(1)(1)Lety=x2−x

⟹(y−20)(y−42)=504⟹(y−20)(y−42)=504

⟹y2−62y+840=504⟹y2−62y+840=504

⟹y2−62y+336=0⟹y2−62y+336=0

⟹y2−56y−6y+336=0∵(−6)(−56)=336⟹y2−56y−6y+336=0∵(−6)(−56)=336

⟹y(y−56)−6(y−56)=0⟹y(y−56)−6(y−56)=0

⟹(y−56)(y−6)=0⟹(y−56)(y−6)=0

⟹y−56=0⟹y=56andy−6=0⟹y=6⟹y−56=0⟹y=56andy−6=0⟹y=6

by using (1)by using (1)

x2−x=56⟹x2−x−56=0⟹x2−8x+7x−56=0x2−x=56⟹x2−x−56=0⟹x2−8x+7x−56=0

⟹x(x−8)+7(x−8)=0⟹(x−8)(x+7)=0⟹x(x−8)+7(x−8)=0⟹(x−8)(x+7)=0

⟹x−8=0∴x=8x+7=0∴x=−7⟹x−8=0∴x=8x+7=0∴x=−7

x2−x=6⟹x2−x−6=0⟹x2−3x+2x−6=0x2−x=6⟹x2−x−6=0⟹x2−3x+2x−6=0

⟹x(x−3)+2(x−3)=0⟹(x−3)(x+2)=0⟹x(x−3)+2(x−3)=0⟹(x−3)(x+2)=0

⟹x−3=0∴x=3x+2=0∴x=−2⟹x−3=0∴x=3x+2=0∴x=−2

Answer 2

2

x−7

×5

x−4

=1250

2

x−7

×5

x−4

=2×625

2

x−7

×5

x−4

=2

1

×5

4

x−7=1

x=8

x−4=4

x=8