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Answer:
The statement is true
see the explanation
Step-by-step explanation:
we have the proportion
![\frac{a}{b}=\frac{c}{d}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bb%7D%3D%5Cfrac%7Bc%7D%7Bd%7D)
we know that
To solve the proportion multiply in cross
so
![(a)(d)=(b)(c)](https://tex.z-dn.net/?f=%28a%29%28d%29%3D%28b%29%28c%29)
![ad=bc](https://tex.z-dn.net/?f=ad%3Dbc)
therefore
The statement is true
B=t-am is the correct answer:)
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Solve the equation:
![\mathsf{\dfrac{8}{x-5}-\dfrac{9}{x-4}=\dfrac{5}{x^2-9x+20}\qquad\qquad(x\ne 5~and~x\ne 4)}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cdfrac%7B8%7D%7Bx-5%7D-%5Cdfrac%7B9%7D%7Bx-4%7D%3D%5Cdfrac%7B5%7D%7Bx%5E2-9x%2B20%7D%5Cqquad%5Cqquad%28x%5Cne%205~and~x%5Cne%204%29%7D)
Reduce the fractions at the left side so that they have the same denominator:
![\mathsf{\dfrac{8(x-4)}{(x-5)(x-4)}-\dfrac{9(x-5)}{(x-4)(x-5)}=\dfrac{5}{x^2-9x+20}}\\\\\\ \mathsf{\dfrac{8x-32}{x^2-4x-5x+20}-\dfrac{9x-45}{x^2-4x-5x+20}=\dfrac{5}{x^2-9x+20}}\\\\\\ \mathsf{\dfrac{8x-32}{x^2-9x+20}-\dfrac{9x-45}{x^2-9x+20}=\dfrac{5}{x^2-9x+20}}\\\\\\ \mathsf{\dfrac{8x-32-(9x-45)}{x^2-9x+20}=\dfrac{5}{x^2-9x+20}}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cdfrac%7B8%28x-4%29%7D%7B%28x-5%29%28x-4%29%7D-%5Cdfrac%7B9%28x-5%29%7D%7B%28x-4%29%28x-5%29%7D%3D%5Cdfrac%7B5%7D%7Bx%5E2-9x%2B20%7D%7D%5C%5C%5C%5C%5C%5C%0A%5Cmathsf%7B%5Cdfrac%7B8x-32%7D%7Bx%5E2-4x-5x%2B20%7D-%5Cdfrac%7B9x-45%7D%7Bx%5E2-4x-5x%2B20%7D%3D%5Cdfrac%7B5%7D%7Bx%5E2-9x%2B20%7D%7D%5C%5C%5C%5C%5C%5C%0A%5Cmathsf%7B%5Cdfrac%7B8x-32%7D%7Bx%5E2-9x%2B20%7D-%5Cdfrac%7B9x-45%7D%7Bx%5E2-9x%2B20%7D%3D%5Cdfrac%7B5%7D%7Bx%5E2-9x%2B20%7D%7D%5C%5C%5C%5C%5C%5C%0A%5Cmathsf%7B%5Cdfrac%7B8x-32-%289x-45%29%7D%7Bx%5E2-9x%2B20%7D%3D%5Cdfrac%7B5%7D%7Bx%5E2-9x%2B20%7D%7D)
Numerators must be equal:
![\mathsf{8x-32-(9x-45)=5}\\\\ \mathsf{8x-32-9x+45=5}\\\\ \mathsf{8x-9x=5+32-45}\\\\ \mathsf{-x=-8}\\\\ \mathsf{x=8}\quad\longleftarrow\quad\textsf{this is the solution.}](https://tex.z-dn.net/?f=%5Cmathsf%7B8x-32-%289x-45%29%3D5%7D%5C%5C%5C%5C%0A%5Cmathsf%7B8x-32-9x%2B45%3D5%7D%5C%5C%5C%5C%0A%5Cmathsf%7B8x-9x%3D5%2B32-45%7D%5C%5C%5C%5C%0A%5Cmathsf%7B-x%3D-8%7D%5C%5C%5C%5C%0A%5Cmathsf%7Bx%3D8%7D%5Cquad%5Clongleftarrow%5Cquad%5Ctextsf%7Bthis%20is%20the%20solution.%7D)
I hope this helps. =)
Tags: <em>rational equation fraction solution algebra</em>
Answer:
≈67.81
Step-by-step explanation: