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प्रश्न
If `x/y = p/q`, prove that `(5x + 7y)/(5x - 7y) = (5p + 7q)/(5p - 7q)`.
सिद्धांत
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उत्तर
Given:
`x/y = p/q`
xq = yp
x = `(yp)/q`
To prove:
`(5x + 7y)/(5x - 7y) = (5p + 7q)/(5p - 7q)`
Proof:
Substitute x = `(yp)/q` in the left side:
`(5x + 7y)/(5x - 7y) = (5((yp)/q) + 7y)/(5((yp)/q) - 7y)`
= `(y((5p)/q + 7))/(y((5p)/q - 7))`
= `((5p)/q + 7)/((5p)/q - 7)`
write 7 as `(7q)/q`
= `((5p + 7q)/q)/((5p - 7q)/q)`
= `(5p + 7q)/(5p - 7q)`
Thus, `(5x + 7y)/(5x - 7y) = (5p + 7q)/(5p - 7q)`
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