Simplify 2/(3x^2+4x-7)+1/(3x^2+19x+28)

Math
23×2+4x-7+13×2+19x+28
Simplify each term.
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Factor by grouping.
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For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=3⋅-7=-21 and whose sum is b=4.
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Factor 4 out of 4x.
23×2+4(x)-7+13×2+19x+28
Rewrite 4 as -3 plus 7
23×2+(-3+7)x-7+13×2+19x+28
Apply the distributive property.
23×2-3x+7x-7+13×2+19x+28
23×2-3x+7x-7+13×2+19x+28
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
2(3×2-3x)+7x-7+13×2+19x+28
Factor out the greatest common factor (GCF) from each group.
23x(x-1)+7(x-1)+13×2+19x+28
23x(x-1)+7(x-1)+13×2+19x+28
Factor the polynomial by factoring out the greatest common factor, x-1.
2(x-1)(3x+7)+13×2+19x+28
2(x-1)(3x+7)+13×2+19x+28
Factor by grouping.
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For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=3⋅28=84 and whose sum is b=19.
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Factor 19 out of 19x.
2(x-1)(3x+7)+13×2+19(x)+28
Rewrite 19 as 7 plus 12
2(x-1)(3x+7)+13×2+(7+12)x+28
Apply the distributive property.
2(x-1)(3x+7)+13×2+7x+12x+28
2(x-1)(3x+7)+13×2+7x+12x+28
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
2(x-1)(3x+7)+1(3×2+7x)+12x+28
Factor out the greatest common factor (GCF) from each group.
2(x-1)(3x+7)+1x(3x+7)+4(3x+7)
2(x-1)(3x+7)+1x(3x+7)+4(3x+7)
Factor the polynomial by factoring out the greatest common factor, 3x+7.
2(x-1)(3x+7)+1(3x+7)(x+4)
2(x-1)(3x+7)+1(3x+7)(x+4)
2(x-1)(3x+7)+1(3x+7)(x+4)
To write 2(x-1)(3x+7) as a fraction with a common denominator, multiply by x+4x+4.
2(x-1)(3x+7)⋅x+4x+4+1(3x+7)(x+4)
To write 1(3x+7)(x+4) as a fraction with a common denominator, multiply by x-1x-1.
2(x-1)(3x+7)⋅x+4x+4+1(3x+7)(x+4)⋅x-1x-1
Write each expression with a common denominator of (x-1)(3x+7)(x+4), by multiplying each by an appropriate factor of 1.
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Multiply 2(x-1)(3x+7) and x+4x+4.
2(x+4)(x-1)(3x+7)(x+4)+1(3x+7)(x+4)⋅x-1x-1
Multiply 1(3x+7)(x+4) and x-1x-1.
2(x+4)(x-1)(3x+7)(x+4)+x-1(3x+7)(x+4)(x-1)
Reorder the factors of (x-1)(3x+7)(x+4).
2(x+4)(3x+7)(x+4)(x-1)+x-1(3x+7)(x+4)(x-1)
2(x+4)(3x+7)(x+4)(x-1)+x-1(3x+7)(x+4)(x-1)
Combine the numerators over the common denominator.
2(x+4)+x-1(3x+7)(x+4)(x-1)
Simplify the numerator.
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Apply the distributive property.
2x+2⋅4+x-1(3x+7)(x+4)(x-1)
Multiply 2 by 4.
2x+8+x-1(3x+7)(x+4)(x-1)
Add 2x and x.
3x+8-1(3x+7)(x+4)(x-1)
Subtract 1 from 8.
3x+7(3x+7)(x+4)(x-1)
3x+7(3x+7)(x+4)(x-1)
Cancel the common factor of 3x+7.
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Cancel the common factor.
3x+7(3x+7)(x+4)(x-1)
Rewrite the expression.
1(x+4)(x-1)
1(x+4)(x-1)
Simplify 2/(3x^2+4x-7)+1/(3x^2+19x+28)

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