Solve the rational equation. 1+1x=90x2

Question

Solve the rational equation.  1+1x=90x2

Mespirst · Accepted Answer

Step 1  Given,  1+1x=90x2  Step 2  On simplification, we get  ⇒x+1x=90x2   [by taking LCM]  ⇒x+1=90x  ⇒x2+x=90  ⇒x2+x−90=0  Step 3  Now solving the obtained quadratic equation:  ⇒x2+10x−9x−90=0  ⇒x(x+10)−9(x+10)=0  ⇒(x+10)(x−9)=0  ⇒x+10=0 or x−9=0  ⇒x=−10 or x=9

Whouldess · Accepted Answer

Step 1: Find the common denominator  1+1x=90x2  xx+1x=90x2  Step 2: Add fractions with a common denominator  x+1x=90x2  Step 3: Multiply all terms by the same number to get rid of the denominators  x2(x+1x)=x2⋅90x2  Step 4: Reduce the multiplied terms in the denominator  x(x+1)=90  Step 5: Write the data as a generalized function  x2+x=90  Step 6: Move the terms to the left of the equation  x2+x−90=0  Step 7: Use the sum of the products  x2+x−90=0  Step 8: Multiply by factors  (x-9)(x+10)=0  Step 9: Create two separate equations  x-9=0  x+10=0  Step 10: Calculation  x=9  x=-10  The solution  x=9  x=-10

Solve the rational equation. 1+\frac{1}{x}=\frac{90}{x^{2}}

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