A)-40/3
B)-7/120
C)7/8
D)8/7
Please explain how you found the answer.
2) Simplify: 8t^2-128/4t^2+36t+80
A)-2(t-4)/t-5
B)t-4/t+5
C)2(t+5)/t-4
D)2(t-4)/t+5
Please explain how you found the answer.
B)-7/120
C)7/8
D)8/7
Please explain how you found the answer.
2) Simplify: 8t^2-128/4t^2+36t+80
A)-2(t-4)/t-5
B)t-4/t+5
C)2(t+5)/t-4
D)2(t-4)/t+5
Please explain how you found the answer.
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1) You first cross multiply.
(8x - 7)(9x + 8) = (9x - 8)(8x + 8)
You next multiply and simplify.
72x^2 + x - 56 = 72x^2 + 8x - 64
You now have to solve for x. Eliminate the 72x^2 from each side and combine like terms.
x - 56 = 8x - 64
7x = 8
x = 8/7
2) You first factor the numerator and denominator.
From the numerator factor out 8: 8(t^2 - 16). From the rule of the difference of squares, factor those: 8(t+4)(t-4)
From the denominator factor out 4: 4(t^2 + 9t + 20). Continued factoring: 4(t+5)(t+4)
Put the numerator over the denominator and simplify.
8(t+4)(t-4) / 4(t+5)(t+4)
The t+4 can be eliminated from the numerator and denominator, and the 8/4 can be simplified into 2/1.
Answer: 2(t-4)/(t+5)
(8x - 7)(9x + 8) = (9x - 8)(8x + 8)
You next multiply and simplify.
72x^2 + x - 56 = 72x^2 + 8x - 64
You now have to solve for x. Eliminate the 72x^2 from each side and combine like terms.
x - 56 = 8x - 64
7x = 8
x = 8/7
2) You first factor the numerator and denominator.
From the numerator factor out 8: 8(t^2 - 16). From the rule of the difference of squares, factor those: 8(t+4)(t-4)
From the denominator factor out 4: 4(t^2 + 9t + 20). Continued factoring: 4(t+5)(t+4)
Put the numerator over the denominator and simplify.
8(t+4)(t-4) / 4(t+5)(t+4)
The t+4 can be eliminated from the numerator and denominator, and the 8/4 can be simplified into 2/1.
Answer: 2(t-4)/(t+5)
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1) You can achieve the answer through cross multiplication. All you have to do is multiply 8x-7 by 9x+8 and 8x+8 by 9x-8. It'll look like this: (8x-7)(9x+8) = (8x+8)(9x-8). Then, use the foil method on each side, combine like terms, and you will get D.
2) Look at top and bottom as separate problems. On top, you can factor out a GCF (greatest common factor, which is 8, and factor furthur using the difference of two squares, so it will be 8(t+4)(t-4). Fro the denominator, you can factor out a 4 and futher factor the polynomial out using trial and error method, so that will turn out to be 4(t+4)(t+5). Then it will look like this: 8(t+4)(t-4)/4(t+4)(t+5). Divide and cancel out what you can and your answer is D.
2) Look at top and bottom as separate problems. On top, you can factor out a GCF (greatest common factor, which is 8, and factor furthur using the difference of two squares, so it will be 8(t+4)(t-4). Fro the denominator, you can factor out a 4 and futher factor the polynomial out using trial and error method, so that will turn out to be 4(t+4)(t+5). Then it will look like this: 8(t+4)(t-4)/4(t+4)(t+5). Divide and cancel out what you can and your answer is D.