What is the simplified form of 3 over 2x minus 5 + 21 over 8 x squared minus 14x minus 15?
Solution:
The above statement can be put mathematically as follows:
3/(2x - 5) + 21/ (8x2 - 14x - 15) --- (1)
The denominator of the term on the right hand side of the + sign can be factorized as follows:
8x2 - 20x + 6x - 15
= 4x(2x - 5) + 3(2x - 5))
= (4x + 3)(2x - 5))
Therefore equation (1) can be rewritten as
3/(2x -5) + 21/(2x - 5)(4x + 3))
= 3(4x + 3) + 21/[(2x - 5)(4x + 3)])
= (12x + 9 + 21)/[(2x - 5)(4x + 3)])
= (12x + 30)/[(2x - 5)(4x + 3)])
= 6(2x + 5)/[(2x - 5)(4x + 3)])
= 6(2x + 5)/(2x - 5)(4x + 3))
What is the simplified form of 3 over 2x minus 5 + 21 over 8 x squared minus 14x minus 15?
Summary:
The simplified for of the given algebraic expression 3 over 2x minus 5 + 21 over 8 x squared minus 14x minus 15 is 6(2x + 5)/(2x - 5)(4x + 3)
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