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

hroncits8y

hroncits8y

Answered question

2021-11-19

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

Answer & Explanation

Mespirst

Mespirst

Beginner2021-11-20Added 17 answers

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+x90=0
Step 3
Now solving the obtained quadratic equation:
x2+10x9x90=0
x(x+10)9(x+10)=0
(x+10)(x9)=0
x+10=0 or x9=0
x=10 or x=9
Whouldess

Whouldess

Beginner2021-11-21Added 11 answers

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)=x290x2
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+x90=0
Step 7: Use the sum of the products
x2+x90=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

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