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Answer:
The transformed quadratic equations are:
1. [tex]x^2-7x+10=0[/tex]
2. [tex]8x^2+25x-200=0[/tex]
Step-by-step explanation:
Our aim here is to transform the given rational equations to quadratic equations.
For the given rational equations
1. [tex]x+\frac{8}{x-2} =1+\frac{4x}{x-2}[/tex]
2. [tex]\frac{2x^2}{5} +\frac{5x}{4} =10[/tex]
Transforming the given rational equations to quadratic equations
1. For the first rational equation, get the LCD of both sides of the equation
[tex]x+\frac{8}{x-2} =1+\frac{4x}{x-2}[/tex]
[tex]\frac{x(x-2)+8}{x-2} =\frac{x-2+4x}{x-2}[/tex]
Multiply both side of the equation by x - 2 and simplify their numerators
[tex]x^2-2x+8=5x-2[/tex]
Transpose 5x and - 2 to the left side of the equation, combine like
terms and simplify
[tex]x^2-5x-2x+8+2=0[/tex]
[tex]x^2-7x+10=0[/tex]
2. The second rational equation is more simple, so we proceed to getting the LCD and use the same steps like the first example.
[tex]\frac{2x^2}{5} +\frac{5x}{4} =10[/tex]
[tex]\frac{4(2x^2)+5(5x)}{20} =10[/tex]
Cross-multiply and simplify the equation
[tex]8x^2+25x=200[/tex]
[tex]8x^2+25x-200=0[/tex]
Therefore, the transformed quadratic equations are [tex]x^2-7x+10=0[/tex] and
[tex]8x^2+25x-200=0[/tex]
To learn more about quadratic equations, just click on the following links:
* Definition of quadratic equation
https://brainly.ph/question/202117
* Solving quadratic equations
https://brainly.ph/question/1687510
* Examples of Non-quadratic equations
https://brainly.ph/question/804674
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