
How do you simplify ?
Answer
459.6k+ views
Hint: In this problem we need to simplify the given fraction. We can observe that the given fraction consists of two quadratic equations in both numerator and denominator. So, we will consider both numerator and denominator individually. First, we will consider the numerator and factorise the quadratic equation. While factoring a quadratic equation we will split the middle term as where . So, we will compare the quadratic equation with the standard form of the quadratic equation and follow the above procedure and split the middle term. Now we will take appropriate terms as common and factorise it. Now we will consider the denominator and use the algebraic formula . Now we will substitute both the values in the given fraction and simplify it to get the required result.
Complete step by step solution:
Given that, .
Considering the numerator which is .
Considering the above equation with , then we will get
, , .
Now the value of is .
Factors of are , , . From these factors we can write
Now splitting the middle term in the given quadratic equation, then we will get
Taking as common from the first two terms and as common from the last two terms, then we will get
Now taking as common from the above equation, then we will get
Now considering the denominator which is .
We can write in the above equation, then we will get
Applying the formula in the above equation, then we will get
From equations and we can write the given fraction as
Cancelling the term which is in both numerator and denominator, then we will get
Hence the simplified form of the given fraction is .
Note: In the above fraction we have the denominator in the form of so we have used the algebraic formula and simplified the fraction. In some cases, in the denominator, we may have a quadratic equation. Then we need to factorise the denominator as we did for the numerator and simplify the fraction.
Complete step by step solution:
Given that,
Considering the numerator which is
Considering the above equation with
Now the value of
Factors of
Now splitting the middle term in the given quadratic equation, then we will get
Taking
Now taking
Now considering the denominator which is
We can write
Applying the formula
From equations
Cancelling the term
Hence the simplified form of the given fraction
Note: In the above fraction we have the denominator in the form of
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