Question

Simplify completely quantity 6 x squared minus 54 x plus 84 over quantity 8 x squared minus 40 x plus 48 divided by quantity x squared plus x minus 56 over quantity 2 x squared plus 12 x minus 32

Answer 1

Could you click on the Equation button below the reply box and use the math editor to repost your question so the problem is clearer?

Answer 2

Yes, hold on..

Answer 3

I will do it separately and combine later...

6x^2 - 54x + 84 = 6(x^2 - 9x + 14) = 6(x - 2)(x - 7)

Answer 4

\[\frac{ 6x^2-54x+84 }{ 8x^2-40x+48 } \div \frac{ x^2+x-56 }{ 2x^2+12x-32 }\]

Answer 5

8x^2 - 40x + 48 = 8(x^2 - 5x + 6) = 8(x - 3)(x - 2)

x^2 + x - 56 = (x + 8)(x - 7)

2x^2 + 12x - 32 = 2(x^2 + 6x - 16) = 2(x + 8)(x - 2)

Put them all together, cancel factors and simplify numerator and denominator.
Note: dividing by a fraction is same as flipping the fraction and multiplying.

Answer 6

\[\frac{ 6(x-2) }{ 8(x-3) } \times \frac{ 2(x+8) }{ x+8 }\ is this right so far??

Answer 7

\[\frac{ 6(x-2)(x-7) }{ 8(x-3)(x-2) } \times \frac{ 2(x+8)(x-2) }{ (x+8)(x-7) } = \frac{ 12(x-2) }{ 8(x-3) } = \frac{ 3(x-2) }{ 2(x-3) }\]

Answer 8

Thanks!!