10 pq
P +q
find the value of
x+5p +x+5q/
x-5p +x-5q
Answers
Answer:
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Step-by-step explanation:
Given:
x=10pq/p+q
To find:
If x=10pq/p+q show that x+5p/x-5p + x+5q/x-5q
Solution:
From given, we have,
x = 10pq/p+q
we need to find x+5p / x-5p + x+5q / x-5q
First, we need to substitute the value of x in given equation,
x+5p / x-5p + x+5q / x-5q
(10pq/p+q)+5p / (10pq/p+q)-5p + (10pq/p+q)+5q / (10pq/p+q)-5q
further solving we get,
\begin{gathered}\dfrac{\frac{10pq}{p+q}+5p}{\frac{10pq}{p+q}-5p}+\dfrac{\frac{10pq}{p+q}+5q}{\frac{10pq}{p+q}-5q}\\=\dfrac{p+3q}{q-p}+\dfrac{3p+q}{p-q}\\=\dfrac{-\left(p+3q\right)}{-\left(q-p\right)}+\dfrac{3p+q}{-\left(q-p\right)}\\=\dfrac{-\left(p+3q\right)+3p+q}{-\left(q-p\right)}\\=-\dfrac{-\left(p+3q\right)+3p+q}{q-p}\\=-\dfrac{2p-2q}{q-p}\\=-\dfrac{-2(q-p)}{q-p}\\=-(-2)\\=2\end{gathered}
p+q
10pq
−5p
p+q
10pq
+5p
+
p+q
10pq
−5q
p+q
10pq
+5q
=
q−p
p+3q
+
p−q
3p+q
=
−(q−p)
−(p+3q)
+
−(q−p)
3p+q
=
−(q−p)
−(p+3q)+3p+q
=−
q−p
−(p+3q)+3p+q
=−
q−p
2p−2q
=−
q−p
−2(q−p)
=−(−2)
=2
∴ x+5p/x-5p + x+5q/x-5q = 2